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

3 Answers

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

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

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