Question

How do you factor the expression `25x^2+70x+49`?

Answer 1

`25x^2+70x+49 = (5x+7)^2`

Explanation:

Given:

`25x^2+70x+49`

Note that:

• Both `25x^2 = (5x)^2` and `49 = 7^2` are perfect squares.

• The middle term is `70x = 2(5x)(7)`.

So the given expression is a perfect square trinomial, matching:

`A^2+2AB+B^2 = (A+B)^2`

with `A=5x` and `B=7`:

`25x^2+70x+49 = (5x)^2+2(5x)(7)+7^2 = (5x+7)^2`

Answer 2

`(5x+7)^2`

Explanation:

`25x^2+70x+40`

=`(5x)^2+2*5x*7+7^2`

=`(5x+7)^2`