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

1 Answer
Nov 5, 2015

Answer:

#-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)#