What is the standard form of y=(2x2+5)(x−2)+(x−4)2?
1 Answer
Dec 25, 2017
Explanation:
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FOIL (First, Outer, Inner, Last) Distribute the binomials.
y=(2x2+5)(x−2)+(x−4)2
y=[(2x2⋅x)+(2x2⋅−2)+(5⋅x)+(5⋅−2)+(x−4)(x−4)]
y=(2x3−4x2+5x−10)+(x2−8x+16) -
Note: A quick shortcut to FOILing squared binomials
(x−4)2 is to square the first term,x→x2 , 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) - Add like terms.
y=2x3−4x2+x2+5x−8x−10+16
y=2x2−3x2−3x−6