Question

What is the standard form of `y= (2x^2+5)(x-2) + (x-4)^2`?

Answer 1

`y=2x^2-3x^2-3x-6`

Explanation:

1. FOIL (First, Outer, Inner, Last) Distribute the binomials.
   `y=(2x^2+5)(x-2)+(x-4)^2`
   `y=[(2x^2*x)+(2x^2*-2)+(5*x)+(5*-2)+(x-4)(x-4)]`
   `y=(2x^3-4x^2+5x-10)+(x^2-8x+16)`

2. Note: A quick shortcut to FOILing squared binomials `(x-4)^2` is to square the first term, `x -> x^2`, multiplying the first time by the last term and then doubling it, `(x-4) -> x*-4*2=-8x`, and then by squaring the last term, `(-4)^2=+16`
   #(x-4)^2=x^2-8x+16)

3. Add like terms.
   `y=2x^3-4x^2+x^2+5x-8x-10+16`
   `y=2x^2-3x^2-3x-6`