What is the standard form of #y= (2x^2+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=(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)# -
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) - Add like terms.
#y=2x^3-4x^2+x^2+5x-8x-10+16#
#y=2x^2-3x^2-3x-6#