Question

Rewrite each expression using the Distributive Property. Then simplify.

$n\left(n-\mathbf{3}{n}^2+\mathbf{2}\right)$

Short answer

$n\left(n-\mathbf{3}{n}^2+\mathbf{2}\right)=-\mathbf{3}{n}^3+n^2+\mathbf{2}n$

Step-by-step solution

Step 1. Write distributive property.

For any numbers a,b and c, $a\left(b+c\right)=ab+ac$.

Step 2. Apply distributive property.

Apply distributive property to the given expression, $n\left(n-3n^2+2\right)$.

$n\cdot n-n\cdot 3n^2+n\cdot 2$

Step 3. Simplify.

Simplify the above obtained expression.

$n^2-3n^3+2n=-3n^3+n^2+2n$

Therefore,$n\left(n-3n^2+2\right)$ can be written using distributive property as$-3n^3+n^2+2n$