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

1 Answer
Dec 25, 2017

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