How do you find the product of #(x + 5)^2#?
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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.
#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.
FOIL(First, Outer, Inner, Last)
Answer: #x^2+10x+25#
#(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#
