Question

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

Answer 1

`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.

Answer 2

`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.

Answer 3

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`