Solve (m+4)^2-4(m+1)^2

$$( m + 4 ) ^ { 2 } - 4 ( m + 1 ) ^ { 2 }$$

Evaluate

$$12-3m^{2}$$

Solution Steps

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

$$m^{2}+8m+16-4\left(m+1\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m+1\right)^{2}.

$$m^{2}+8m+16-4\left(m^{2}+2m+1\right)$$

Use the distributive property to multiply -4 by m^{2}+2m+1.

$$m^{2}+8m+16-4m^{2}-8m-4$$

Combine m^{2} and -4m^{2} to get -3m^{2}.

$$-3m^{2}+8m+16-8m-4$$

Combine 8m and -8m to get 0.

$$-3m^{2}+16-4$$

Subtract 4 from 16 to get 12.

$$-3m^{2}+12$$

Expand

$$12-3m^{2}$$

Solution Steps

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

$$m^{2}+8m+16-4\left(m+1\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m+1\right)^{2}.

$$m^{2}+8m+16-4\left(m^{2}+2m+1\right)$$

Use the distributive property to multiply -4 by m^{2}+2m+1.

$$m^{2}+8m+16-4m^{2}-8m-4$$

Combine m^{2} and -4m^{2} to get -3m^{2}.

$$-3m^{2}+8m+16-8m-4$$

Combine 8m and -8m to get 0.

$$-3m^{2}+16-4$$

Subtract 4 from 16 to get 12.

$$-3m^{2}+12$$