Solve (m^2+2)^2-12(m^2+2)+36=

$$( m ^ { 2 } + 2 ) ^ { 2 } - 12 ( m ^ { 2 } + 2 ) + 36 =$$

Evaluate

$$\left(m^{2}-4\right)^{2}$$

Solution Steps

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

$$\left(m^{2}\right)^{2}+4m^{2}+4-12\left(m^{2}+2\right)+36$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$m^{4}+4m^{2}+4-12\left(m^{2}+2\right)+36$$

Use the distributive property to multiply -12 by m^{2}+2.

$$m^{4}+4m^{2}+4-12m^{2}-24+36$$

Combine 4m^{2} and -12m^{2} to get -8m^{2}.

$$m^{4}-8m^{2}+4-24+36$$

Subtract 24 from 4 to get -20.

$$m^{4}-8m^{2}-20+36$$

Add -20 and 36 to get 16.

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

Expand

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

Solution Steps

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

$$\left(m^{2}\right)^{2}+4m^{2}+4-12\left(m^{2}+2\right)+36$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$m^{4}+4m^{2}+4-12\left(m^{2}+2\right)+36$$

Use the distributive property to multiply -12 by m^{2}+2.

$$m^{4}+4m^{2}+4-12m^{2}-24+36$$

Combine 4m^{2} and -12m^{2} to get -8m^{2}.

$$m^{4}-8m^{2}+4-24+36$$

Subtract 24 from 4 to get -20.

$$m^{4}-8m^{2}-20+36$$

Add -20 and 36 to get 16.

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