Question

What is the standard form of `y= (2x+8)^3-(5x-3)^2`?

Answer 1

`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.