What is the standard form of # y= (2x+8)^3-(5x-3)^2#?
1 Answer
May 2, 2016
#y = 8x^3+71x^2+414x+503#
Explanation:
Multiply out and simplify, using the binomial expansions:
#(a+b)^3 = a^3+3a^2b+3ab^2+b^3#
#(a+b)^2 = a^2+2ab+b^2#
as follows:
#y = (2x+8)^3-(5x-3)^2#
#= ((2x)^3+3(2x)^2(8)+3(2x)8^2+8^3)-((5x)^2-2(5x)(3)+3^2)#
#=(8x^3+96x^2+384x+512)-(25x^2-30x+9)#
#=8x^3+(96-25)x^2+(384+30)x+(512-9)#
#=8x^3+71x^2+414x+503#
Standard form consists of a sum of terms in decreasing order of degree, as we have arrived at.
