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

Nov 5, 2015

$- 12 {x}^{4} + 4 {x}^{3} - 4 {x}^{2}$

#### 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: ${x}^{2} \cdot {x}^{3} \implies \left(x \cdot x\right) \cdot \left(x \cdot x \cdot x\right)$ Essentially, it would be ${x}^{5}$, or the initial exponents sum.

So, using the distributive property, we can start with $- 4 {x}^{2} \cdot 3 {x}^{2}$, which comes out to be $\textcolor{red}{- 12 {x}^{4}}$, as $- 4 \cdot 3$ is $- 12$ and the exponents add as I explained above.

The next one is $- 4 {x}^{2} \cdot - x$, which is $\textcolor{b l u e}{4 {x}^{3}}$. 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 $- 4 {x}^{2} \cdot 1$. Anything multiplied by 1 is itself, so it is $\textcolor{g r e e n}{- 4 {x}^{2}}$.

The final step is to add each bit together. $\textcolor{red}{- 12 {x}^{4}} \textcolor{b l u e}{+ 4 {x}^{3}} \textcolor{g r e e n}{- 4 {x}^{2}}$