How do you simplify -4x^2(3x^2 - x + 1) ?

1 Answer
Nov 5, 2015

-12x^4 + 4x^3 - 4x^2

Explanation:

I will start out explaining that when you multiply an exponent by an exponent, it adds each exponent to each other. Here is a visual representation of this: x^2 * x^3 => (x * x) * (x * x * x) Essentially, it would be x^5, or the initial exponents sum.

So, using the distributive property, we can start with -4x^2 * 3x^2, which comes out to be color(red)(-12x^4), as -4 * 3 is -12 and the exponents add as I explained above.

The next one is -4x^2 * -x, which is color(blue)(4x^3). It is positive because of the two negatives multiplied by each other, and the exponent is x^3 because anything without an exponent, we can assume has a power of 1 (anything to the power of 1 is itself).

The final one is -4x^2 * 1. Anything multiplied by 1 is itself, so it is color(green)(-4x^2).

The final step is to add each bit together. color(red)(-12x^4) color(blue)(+4x^3)color(green)( - 4x^2)