Question

How do you factor the expression `20x^2 + 60 x + 45`?

Answer 1

`20x^2 +60x +45`

`=5(4x^2 +12x+9)`

`=5(4x^2 +6x +6x+9)`

`=5 (2x(2x+3) + 3(2x+3))`

`=5 (2x+3)(2x+3)`

ALTERNATIVELY,

`20x^2 +60x+45`

`=5(4x^2+12x+9)`

`=5((2x)^2 +2*2x*3 +3^2))`

`=5(2x+3)^2`

Answer 2

`(10x+15)(2x+3)=5(2x+3)^2`

Explanation:

We have the quadratic expression `20x^2+60x+45`.

This is of the form `ax^2+bx+c`, and here, `a=20, b=60, c=45`.

First we must find `axxc`. Here, `axxc=20xx45=900`

Now, we must find two factors of `axxc=900`, that add up to give `b`.

You can do this fast after loads of practice, and I'm just going to go and say it: The factors are `30` and `30`. They multiply to give `900`, and add up to give `60`. We can write our equation as:

`20x^2+30x+30x+45`

`=10x(2x+3)+15(2x+3)`

`=(10x+15)(2x+3)`

`=5(2x+3)(2x+3)`

`=5(2x+3)^2`

Hence factored.