Question

Find each sum or difference.

$\left(\mathbf{7}m-\mathbf{8}{n}^2+\mathbf{3}n\right)-\left(-\mathbf{2}{n}^2+\mathbf{4}m-\mathbf{3}n\right)$

Short answer

The difference of$\left(7m-8n^2+3n\right)-\left(-2n^2+4m-3n\right)$ is $-\mathbf{6}{n}^2+\mathbf{3}m+\mathbf{6}n$.

Step-by-step solution

Step 1. Write steps to subtract polynomials.

Following are the steps to subtract polynomials.

1. Subtract the number by adding its additive inverse.

2. Group like terms.

3. Combine like terms by using horizontal or vertical format.

Step 2. Add additive inverse.

Subtract$-2n^2+4m-3n$ by adding its additive inverse.

$\left(7m-8n^2+3n\right)+\left(2n^2-4m+3n\right)$

Step 3. Group like terms.

Group like terms in the given expression.

$\left(-8n^2+2n^2\right)+\left(7m-4m\right)+\left(3n+3n\right)$

Step 4. Combine like terms.

Combine like terms in expression in horizontal format.

$-6n^2+3m+6n$

Therefore, the difference of$\left(7m-8n^2+3n\right)-\left(-2n^2+4m-3n\right)$ is $-6n^2+3m+6n$.