How do you find the product of #(x + 5)^2#?

3 Answers

Answer:

#x^2 + 10x + 25#

Explanation:

We can use Binomial Expansion to find the product.

The Binomial Theorem States that,

For Any Integer #n gt 0#,

#(x + y)^n =# #(n# combination #0)x^n + (n# combination #1)x^(n-1)y^1# + .............. + #(n# combination #n-1)x^1y^(n-1) + (n# combination #n)y^n#

So, Here, use can use the formula.

#(x + 5)^2 =# #(2# combination #0)x^2 + (2# combination #1)x^(2-1)5^1# + #(2# combination #1)x^1 5^(2-1) + (2# combination #2)5^2#

= #1 xx x^2 + 1 xx x * 5 + 1 xx x* 5 + 1 xx 5^2#

[You should learn Permutations And Combinations Prior to this step.]

= #x^2 + 5x + 5x + 25#

=#x^2 + 10x + 25#

Hope this helps.

Mar 20, 2018

Answer:

#x^2 + 10x + 25#

Explanation:

#color(white)(xx)(x + 5)^2#

#= (x + 5)(x + 5)# [Break it up]

#= x(x + 5) + 5(x + 5)# [Multiply]

#= (x^2 + 5x) +(5x + 25)# [Distributive Property]

#= x^2 + 5x + 5x + 25#

#= x^2 + 10x + 25# [Add everything up]

Hence Explained.

Mar 20, 2018

Answer:

FOIL(First, Outer, Inner, Last)
Answer: #x^2+10x+25#

Explanation:

#(x+5)^2=(x+5)(x+5)#
First- Multiply #x*x# to get #x^2#
Outer- #x*5=5x#
Inner- #5*x=5x#
Last- #5*5=25#
We know have #x^2+5x+5x+25#
#5x+5x=10x#
#x^2+10x+25#