# Pascal's Triangle and Binomial Expansion

### Topic Page

Pascal's Triangle and Binomial Expansion### Questions

- What is Pascal's triangle?
- How do I find the #n#th row of Pascal's triangle?
- How does Pascal's triangle relate to binomial expansion?
- How do I find a coefficient using Pascal's triangle?
- How do I use Pascal's triangle to expand #(2x + y)^4#?
- How do I use Pascal's triangle to expand #(3a + b)^4#?
- How do I use Pascal's triangle to expand #(x + 2)^5#?
- How do I use Pascal's triangle to expand #(x - 1)^5#?
- How do I use Pascal's triangle to expand a binomial?
- How do I use Pascal's triangle to expand the binomial #(a-b)^6#?
- How do I use Pascal's triangle to expand the binomial #(d-3)^6#?
- How do I use Pascal's triangle to expand the binomial #(d-5)^6#?
- How do I use Pascal's triangle to expand the binomial #(d-5y)^6#?
- How do I find the constant term of a binomial expansion?
- How do I find the #n#th term of a binomial expansion?
- How do I find the binomial expansion of #(2x+1)^3#?
- How do I find the binomial expansion of #(2x+1)^4#?
- How do I find the binomial expansion of #(3x-2)^4#?
- How do I find the binomial expansion of #(8-9x)^(1/3)#?
- How do I find the binomial expansion of #(1+12x)^(3/4)#?
- What is the binomial expansion of #(2x+1)^4#?
- What is the binomial expansion of #(2x + 3)^5#?
- What is the binomial expansion of #(2x-1)^5#?
- What is the binomial expansion of #(x + 2y)^7#?
- Question #b94a3
- What is the middle term in the expansion of #(x/2-2y)^6#?
- How do you find the binomial expansion of #(3x-2)^4#?
- How do you find the binomial expansion of #(2x-1)^5#?
- How do you find the binomial expansion of #(x + 2)^4#?
- How do you find the binomial expansion of #(x + 2y)^7#?
- How do you find the binomial expansion of #(x + y)^7#?
- How do you find the binomial expansion of #(x-2y)^6#?
- How do you find the in binomial expansion of #(a + 2)^4 #?
- How do you find the in binomial expansion of #(x-3)^5 #?
- What is the binomial expansion of (2x+3)^4?
- What is the binomial expansion of #(a^2 + 2)^4#?
- How do you find the binomial expansion of the expression #(d-5)^6#?
- How do you find the binomial expansion of the expression #(x+3y)^7#?
- What is the 4th term of #(3x+y)^7#?
- What is the last term of #(2x+y)^20#?
- How do you find the fourth term of #((2x-z)^2 )^6#?
- What is the binomial expansion of #(x+2)^5#?
- What is the coefficient of #x^8 y^5# in the expansion of #(x+y)^13#?
- What is the Binomial Expansion of #(1+r)^-1#?
- What is the Binomial Expansion of #(d+3)^7#?
- What is the Binomial Expansion of #(2k+x)^n#?
- What is the Binomial Expansion of #(2+x)^4#?
- What is the Binomial Expansion of #(A+3B)^4#?
- How do you find the 7th term in the binomial expansion for #(x - y)^6#?
- How do you find the 4th term in the binomial expansion for #(x - 10z)^7#?
- How do you find the 5th term in the binomial expansion for #(5a + 6b)^5#?
- How do you find the binomial expansion for #(2x+3)^3#?
- How do you find the binomial expansion for #((x-(2/x^2))^9#?
- What is the fourth term in the expansion of #(2x-y)^5#?
- What is the third term in the expansion of# (cos x+3)^5#?
- What is the binomial expansion of #(2 + 3x)^-2#?
- What is the binomial expansion of #(1-2x)^(1/3) #?
- What is coefficient of the #x^3# term in the binomial expansion of #(4 - x)^9#?
- What is coefficient of the #x^4# term in the binomial expansion of # (x^2-1)^12#?
- What is the binomial expansion of #(2x+1/x)^7 #?
- If the coefficient of #x^3# in the expansion of #(2 + x)(3 - ax)^4# is 30, how do you find the values of the constant a?
- What is row 1 in Pascals triangle?
- The 4th number in the 32nd row of pascals triangle is the sum of how many triangular numbers?
- How do you expand the equation #(4x+y)^4# using pascals triangle?
- What is the 40th row and the sum of all the numbers in it of pascals triangle?
- What is the Pascal triangle up to 30 rows?
- How do you use pascals triangle to expand (3y-4x)^4?
- How do you use pascals triangle to expand #(2x-y)^5#?
- How do you use pascals triangle to expand #(2x-3)^5 #?
- How do you use pascals triangle to expand #(x-3)^5 #?
- How do you use pascals triangle to expand #(3a-b)^4#?
- What are the uses of pascal's triangle in real life?
- What is the 50th row of Pascal's Triangle?
- How do you use pascals triangle to expand #(2s+1)^4#?
- How do you use pascals triangle to expand #(2a + 1)^5#?
- How do you use pascals triangle to expand #(x^2 - 2)^4#?
- How do you use pascals triangle to expand # (d - 5)^6#?
- How do you use pascals triangle to expand #(d + 5)^7#?
- How do you use pascals triangle to expand #(d + 4)^7#?
- How do you use pascals triangle to expand #(x^2+5)^6#?
- How do you use pascals triangle to expand # (2x-6)^7#?
- How do you use pascals triangle to expand #(2x-3y)^3#?
- How do you use pascals triangle to expand #(x-5)^6#?
- How many odd numbers are IN the 100th row of pascals triangle?
- How do you use pascals triangle to expand #(x+2)^5 #?
- How do you use pascals triangle to expand #(2y-x)^5#?
- How do you use pascals triangle to expand # (x^3 + 5y)^4#?
- Why does the sixth row go 1, 6, 15, 20, 15, 6, 1?
- How do you use pascals triangle to expand #(x+4)^3#?
- How do you use pascals triangle to expand #(2x-y)^3#?
- How do you use pascals triangle to expand # (d-5y)^6#?
- How do you expand #(x + 3)^6# using Pascal’s Triangle?
- How do you expand (4x – 3y)^4# using Pascal’s Triangle?
- How do you expand #(r+3)^5# using Pascal’s Triangle?
- How do you expand #(2x-y)^5# using Pascal’s Triangle?
- How do you expand # (d - 5)^6# using Pascal’s Triangle?
- How do you expand # (d-4)^6# using Pascal’s Triangle?
- How do you expand #(d + 5)^7# using Pascal’s Triangle?
- How do you expand #(4x+y)^4# using Pascal’s Triangle?
- How do you expand #(x-5)^6 # using Pascal’s Triangle?
- How do you expand #(1+2x)^6# using Pascal’s Triangle?
- How do you expand #(1+x^3)^4# using Pascal’s Triangle?
- How do you expand #(3x+2)^3# using Pascal’s Triangle?
- How do you expand #(3a-b)^4 # using Pascal’s Triangle?
- How do you expand #(3x-5y)^6# using Pascal’s Triangle?
- How do you expand #(x-3)^5# using Pascal’s Triangle?
- How do you expand #(2x-3)^5 # using Pascal’s Triangle?
- How do you expand # (2x + y)^4 # using Pascal’s Triangle?
- How do you expand # (3a +b)^4 # using Pascal’s Triangle?
- How do you expand #(x + 2)^5# using Pascal’s Triangle?
- How do you expand # (x + y)^6# using Pascal’s Triangle?
- What is the number of terms of the expanded form of (x+3y)^7?
- How do you expand #(x + 3)^5#?
- How do you expand #(3a – b)^6#?
- What is the 5th term of #(s + t)^9#?
- How do you find the 6th term of #(a + b)^8# ?
- What is the fifth term of #(x + y)^8#?
- How do you find the eight term in the expansion #(a + b)^14#?
- How many sandwiches are possible if the restaurant lets you build a sandwich by choosing any 4 of 10 sandwich toppings?
- If there are 6 soups to choose from , how many soup- and build a sandwich specials are there?
- An inline skate has 4 wheels. How many ways could 4 replacement wheels be chosen from a pack of 10 wheels and fitted to a skate?
- A combination lock will open when the right choice of three numbers (from 1-40, inclusive) is selected. How many different lock combinations are possible?
- What is the coefficient of #x^2# in the expansion of #(x+2)^3#?
- Question #34e4f
- How do you use the pascals triangle to expand #(x + 2)^5#?
- How do you find the coefficient of #x^7" in "(1+x)^11#?
- How do you find the coefficient of #x^2# in the expansion of #(2+x)^5#?
- How do you find the coefficient of #x^2# in the expansion of #(x+2)^5#?
- How do you find the coefficient of #x^2# in the expansion of #(x+3)^5#?
- How do you find the coefficient of #x^3y^2# in the expansion of #(x-3y)^5#?
- How do you find the coefficient of #a^2# in the expansion of #(2a+1)^5#?
- How do you find the 2nd term in the expansion of #(y-2x)^4#?
- How do you find the 4th term in the expansion of #(4y+x)^4#?
- How do you find the 1st term in the expansion of #(a+b)^5#?
- How do you find the 2nd term in the expansion of #(y-x)^4#?
- How do you expand #(2m-1)^4#?
- How do you expand #(x-y)^3#?
- How do you expand #(2x^3+1)^5#?
- How do you expand #(y-x^2)^3#?
- How do you expand #(x^3-1/x^2)^3#?
- How do you expand #(1-0.1)^3#?
- How do you expand #(u-v)^3#?
- How do you expand #(m+2n)^4#?
- How do you expand #(y+x)^4#?
- How do you expand #(2+b^2)^4#?
- How do you expand #(4a^3+1)^4#?
- How do you expand #(y+4)^2#?
- How do you expand #(m+n)^5#?
- How do you expand #(5y^4-x)^3#?
- How do you expand #(2x^4-1)^6#?
- How do you expand #(2y+1)^6#?
- How do you expand #(x^4-y^3)^3#?
- How do you expand #(x+2)^7#?
- How do you expand #(x-y)^4#?
- How do you expand #(2u^4+1)^4#?
- How do you expand #(x+2y)^7#?
- How do you expand #(y-3x^2)^2#?
- How do you expand #(3u-1)^5#?
- How do you expand #(x-9y)^2#?
- How do you expand #(1-2b^4)^5#?
- How do you expand #(2y-x^4)^6#?
- How do you expand #(5u^2-1)^3#?
- How do you expand #(3v^4+1)^3#?
- How do you expand #(y^4+2x)^7#?
- How do you expand #(1+4x^4)^4#?
- How do you expand #(2y^2+x)^7#?
- How do you expand #(1+4x^4)^4#?
- How do you expand #(2y^2+x)^7#?
- How do you expand #(6y^4-1)^2#?
- How do you expand #(3v^2-1)^4#?
- How do you expand #(10y^3+1)^2#?
- How do you expand #(2y^3+x)^5#?
- How do you expand #(y^3-2x^4)^5#?
- How do you expand #(5m^3-1)^3#?
- If one of the terms of the binomial expression #(x+y-3z)^n# is #A*x^3*y^4*z^2# , what is #n# ?
- How do you expand the binomial #(x+1)^4#?
- How do you expand the binomial #(2x+4)^3#?
- How do you expand the binomial #(x-y)^5#?
- How do you expand the binomial #(x-2)^3#?
- How do you expand the binomial #(3x-1)^4#?
- How do you expand the binomial #(4x-4y)^3#?
- How do you expand the binomial #(x+4)^6# using the binomial theorem?
- How do you expand the binomial #(x-3y)^6# using the binomial theorem?
- How do you expand the binomial #(x^2+y)^7# using the binomial theorem?
- How do you expand the binomial #(2x-y^3)^7# using the binomial theorem?
- How do you expand the binomial #(x-2)^3# using the binomial theorem?
- How do you expand the binomial #(x+4)^5# using the binomial theorem?
- How do you expand the binomial #(x+3y)^4# using the binomial theorem?
- How do you expand the binomial #(2x-y)^6# using the binomial theorem?
- How do you expand the binomial #(x^3+3)^5# using the binomial theorem?
- How do you expand the binomial #(3x^2-3)^4# using the binomial theorem?
- How do you expand the binomial #(2x-y^2)^7# using the binomial theorem?
- How do you expand the binomial #(x^3+y^2)^3# using the binomial theorem?
- How do you find the coefficient of #x^5# in the expansion of #(x-3)^7#?
- How do you find the coefficient of #x^4# in the expansion of #(x+2)^8#?
- How do you find the coefficient of #x^6# in the expansion of #(x^2+4)^10#?
- How do you expand #(3x+2)^9# using the binomial theorem?
- How do you find the coefficient of #x^2# in the expansion of #(2+x)^5#?
- How do you find the coefficient of #x# in the expansion of #(x+3)^5#?
- How do you expand #(2x+5)^7#?
- How do you expand #(x^2+3)^6#?
- How do you find the 10th term of #(x+3)^12#?
- How do you find the 5th term of #(4x-y)^8#?
- How do you expand #(2x+3y)^4#?
- How do you expand #(3x+3y)^3#?
- How do you expand #(5x+4y)^2#?
- How do you expand #(2x+2y)^4#?
- How do you expand #(8x+4y)^2#?
- How do you expand #(9x+8y)^1#?
- How do you expand #(4x+3y)^2#?
- How do you expand #(5x+2y)^3#?
- How do you expand #(a+2b)^4#?
- How do you expand #(x-y)^6#?
- How do you expand #(c+1/c)^4#?
- How do you expand #(d-1/d)^5#?
- How do you expand #(x+y)^10#?
- How do you expand #(x-y)^10#?
- How do you expand #(z+1/z)^8#?
- How do you expand #(w^2+1/w)^9#?
- How do you find the third term of #(x^2-2)^7#?
- How do you find the third term of #(c-d)^8#?
- How do you find the third term of #(x/3-3/x)^12#?
- How do you find the third term of #(4x-2/x)^8#?
- How do you find three consecutive binomial coefficients in the relationship #1:2:3#?
- How do you find three consecutive binomial coefficients in the relationship #1:2:3#?
- What is the 6th term in the expansion of #(3a^2 - 2b)^10#?
- Find a particular solution for the differential equation #y''-4y'+8y-((2x^2-3x)e^{2x}cos(2x)+(10x^2-x-1)e^{2x}sin(2x))=0# ?
- What is the 2nd term in expansion of #(3u-1)^3#?
- Question #10746
- Question #00978
- If in the expansion of #(1+ax)^n# coefficient of #x^3# is six times that of #x^2#, find #a# and #n#?
- Expand #(2x+3)^3# using binomial expansion?
- How do use the binomial theorem to calculate 6C4?
- How do use the binomial theorem to calculate 10C7?
- How do use the binomial theorem to calculate #""^8C_5#?
- How do you use Pascal's triangle to calculate the binomial coefficient of #((7), (3))#?
- How do you use Pascal's triangle to calculate the binomial coefficient of #((9), (4))#?
- How do you use Pascal's triangle to calculate the binomial coefficient of #((5), (3))#?
- How do you use the Binomial theorem to expand #(a-3b)^5#?
- How do you use the Binomial theorem to expand #(3x+y^2)^7#?
- How do you use the Binomial theorem to expand #(5+2i)^4#?
- How do you use the Binomial theorem to expand #(4-5i)^3#?
- Expand #(x^2+3y)^7# using Pascal's triangle ?
- How do you express #(sin 4 theta)/(sin theta)# in terms of #sin theta# and #cos theta# ?
- Find the coefficient of #x^7# in the expansion of #(1-x)^(-2)#?
- What is the value of n?
- By using the binomial expansion of #(1+i)^(2n)# can you prove that: #( ""_0^(2n)) - ( ""_2^(2n)) + ( ""_4^(2n)) - ( ""_6^(2n)) + .... + (-1)^n( ""_(2n)^(2n)) = 2^ncos((npi)/2), n in ZZ^+#?
- Find the constant term in this binomial expansion?
- Expanding this binomial?
- Question #69c6c
- In the binomial expansion of (a+b)^n the coefficients of the terms equidistant from the beginning and the ending are always..? I know the answer is EQUAL. But how?
- How do you use Binomial Theorem or Pascal's Triangle to expand #(2x-y)^5#?
- What is the coefficient of the term in #x^9# in the expansion of #(3+x^3)^5# ?
- Question #575cd
- Question #69db0
- If #( 1 + x )^n = C_0 + C_1 x_1 + C_2 x_2 + ⋯ + C_n x_n# then show that #C_0C_r+C_1C_(r+1)+C_2C_(r+2)+....C_nC_(r+n)=((2n)!)/((n+r)!(n-r)!) ?#
- Question #ed4ea
- Question #51696
- Question #832b7
- Find the binomial expansion of #(3x-5/x^3)^7# in ascending power of #x#?
- Find the first 3 and last 3 terms in the expansion #(2x-1)^11# using the binomial theorem?