Question

What is the standard form of `y=(x+4)(2x-3) -3x^2`?

Answer 1

The standard form is `y=-x^2+5x-12`.

Explanation:

`y=(x+4)(2x-3)-3x^2`

The standard form for a quadratic equation is `ax^2+bx+c`, where `a, b, and c` are coefficients.

First Foil the two binomials.

`(x+4)(2x-3)`

`a=x, b=4, c=2x, d=-3`

`(x+4)(2x-3)=ac+ad+bc+bd`

`(x+4)(2x-3)=(x*2x)+(x*-3)+(4*2x)+(4*-3)`

`(x+4)(2x-3)=(2x^2)+(-3x)+(8x)+(-12)`

Combine like terms.

`(x+4)(2x-3)=2x^2+5x-12`

Return to original equation, keeping the foiled results.

`y=2x^2+5x-12-3x^2`

Combine like terms.

`y=2x^2-3x^2+5x-12`

`y=-x^2+5x-12`