What is the standard form of y=(2x2+5)(x2)+(x4)2?

1 Answer
Dec 25, 2017

y=2x23x23x6

Explanation:

  1. FOIL (First, Outer, Inner, Last) Distribute the binomials.
    y=(2x2+5)(x2)+(x4)2
    y=[(2x2x)+(2x22)+(5x)+(52)+(x4)(x4)]
    y=(2x34x2+5x10)+(x28x+16)

  2. Note: A quick shortcut to FOILing squared binomials (x4)2 is to square the first term, xx2, multiplying the first time by the last term and then doubling it, (x4)x42=8x, and then by squaring the last term, (4)2=+16
    #(x-4)^2=x^2-8x+16)

  3. Add like terms.
    y=2x34x2+x2+5x8x10+16
    y=2x23x23x6