Solve 6m(m+n)-(-m-4n)^2

$$6 m ( m + n ) - ( - m - 4 n ) ^ { 2 }$$

Evaluate

$$\left(m-2n\right)\left(5m+8n\right)$$

Solution Steps

Use the distributive property to multiply 6m by m+n.

$$6m^{2}+6mn-\left(-m-4n\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-m-4n\right)^{2}.

$$6m^{2}+6mn-\left(\left(-m\right)^{2}-8\left(-m\right)n+16n^{2}\right)$$

Calculate -m to the power of 2 and get m^{2}.

$$6m^{2}+6mn-\left(m^{2}-8\left(-m\right)n+16n^{2}\right)$$

Multiply -8 and -1 to get 8.

$$6m^{2}+6mn-\left(m^{2}+8mn+16n^{2}\right)$$

To find the opposite of m^{2}+8mn+16n^{2}, find the opposite of each term.

$$6m^{2}+6mn-m^{2}-8mn-16n^{2}$$

Combine 6m^{2} and -m^{2} to get 5m^{2}.

$$5m^{2}+6mn-8mn-16n^{2}$$

Combine 6mn and -8mn to get -2mn.

$$5m^{2}-2mn-16n^{2}$$

Expand

$$5m^{2}-2mn-16n^{2}$$

Solution Steps

Use the distributive property to multiply 6m by m+n.

$$6m^{2}+6mn-\left(-m-4n\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-m-4n\right)^{2}.

$$6m^{2}+6mn-\left(\left(-m\right)^{2}-8\left(-m\right)n+16n^{2}\right)$$

Calculate -m to the power of 2 and get m^{2}.

$$6m^{2}+6mn-\left(m^{2}-8\left(-m\right)n+16n^{2}\right)$$

Multiply -8 and -1 to get 8.

$$6m^{2}+6mn-\left(m^{2}+8mn+16n^{2}\right)$$

To find the opposite of m^{2}+8mn+16n^{2}, find the opposite of each term.

$$6m^{2}+6mn-m^{2}-8mn-16n^{2}$$

Combine 6m^{2} and -m^{2} to get 5m^{2}.

$$5m^{2}+6mn-8mn-16n^{2}$$

Combine 6mn and -8mn to get -2mn.

$$5m^{2}-2mn-16n^{2}$$