Question

How do you factor `100+4x^2-16y-40x`?

Answer 1

If the `-16y` should have been `-16y^2`, then we find:

`100+4x^2-16y^2-40x = 4(x-2y-5)(x+2y-5)`

Explanation:

For the record: I think the question should have specified `-16y^2` rather than `-16y`. Here's what happens if that is the case:

The difference of squares identity can be written:

`a^2-b^2 = (a-b)(a+b)`

Use this with `a=(x-5)` and `b=2y` as follows:

`100+4x^2-16y^2-40x = 4(x^2-10x+25-4y^2)`

`color(white)(100+4x^2-16y^2-40x) = 4(x^2-2x(5)+5^2-4y^2)`

`color(white)(100+4x^2-16y^2-40x) = 4((x-5)^2-(2y)^2)`

`color(white)(100+4x^2-16y^2-40x) = 4((x-5)-2y)((x-5)+2y)`

`color(white)(100+4x^2-16y^2-40x) = 4(x-2y-5)(x+2y-5)`