Question

The simplest form of 7x²-5x(x+2)

Answer 1

factored form:
`2x(x-5)`, standard form:
`2x^2-10x`

Explanation:

so we're given the expression:
`7x^2 - 5x(x+2)`

In this case we want to use the distributive property, which essentially states that:
`a(b+c)=ab+ac`

So we can use this to rewrite:

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

which simplifies to

`-5x^2-10x`

this just simplifies the last part of our expression, so using this instead of what we originally had gives us

`7x^2-5x^2-10x`

Since the 7x^2 and the -5x^2 have the same variable, we can subtract their coefficients.

Another way to think of it is

`7x^2-5x^2\implies x^2(7-5)`

so in a way we're "factoring" out the x^2, which means we can simply subtract the coefficients for this reason.

This of course gives us 2, by we're multiplying by x^2 so we get

`2x^2-10x`

Now if you want you can factor out a 2x, to get

`2x(x-5)`