How do you multiply #(x+4)^3#?

2 Answers
Jul 4, 2017

Answer:

See a solution process below:

Explanation:

We can use Pascal's triangle to solve this problem.

The triangle values for the exponent 3 are:

#1color(white)(.........)3color(white)(.........)3color(white)(.........)1#

Therefore #(x + 4)^3# can be multiplied as:

#(1 xx x^3) + (3 xx 4x^2) + (3 xx 4^2x) + (1 xx 4^3)#

#x^3 + 12x^2 + 48x + 64#

Jul 4, 2017

Answer:

#x^3+12x^2+48x+64#

Explanation:

#"factors of the form"#

#(x+a)(x+b)(x+c)" can be expanded as"#

#x^3+(a+b+c)x^2+(ab+ac+bc)x+abc#

#rArr(x+4)^3=(x+4)(x+4)(x+4)#

#"with " a=b=c=4#

#rArr(x+4)^3#

#=x^3+(4+4+4)x^2+(16+16+16)x+4^3#

#=x^3+12x^2+48x+64#