What is the standard form of y= (4x-2x^2)(-4x+3) -(x-4)^3?

1 Answer
Jun 23, 2018

7x^3-10x^2-36x+64

Explanation:

In order to complete this problem (and make it easier on ourselves), we should split it into two parts. Let's start with the first part, (4x-2x^2)(-4x+3). Using FOIL (First, Outsides, Insides, Last), we can simplify this down:

(4x)(-4x)+(4x)(3)+(-2x^2)(-4x)+(-2x^2)(3)
-16x^2+12x+8x^3-6x^2

We don't need to write this in standard form quite yet as we still have the other half of the equation, (x-4)^3. The formula for the multiplication of (a-b)^3 is a^3+3a^2b+3ab^2+b^3. Let's use this as a guideline for our multiplication.

(x-4)^3
x^3+(3)(x^2)(-4)+(3)(x)(-4)^2+(-4)^3
x^3-12x^2+48x-64

Let's now combine our two parts to create one answer:

-16x^2+12x+8x^3-6x^2-(x^3-12x^2+48x-64)
-16x^2+12x+8x^3-6x^2-x^3+12x^2-48x+64
8x^3-x^3-16x^2-6x^2+12x^2+12x-48x+64
7x^3-10x^2-36x+64