Solve (-6m-3m^2)^2

$$( - 6 m - 3 m ^ { 2 } ) ^ { 2 }$$

Evaluate

$$9\left(m\left(m+2\right)\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-6m-3m^{2}\right)^{2}.

$$36m^{2}+36mm^{2}+9\left(m^{2}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$36m^{2}+36m^{3}+9\left(m^{2}\right)^{2}$$

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

$$36m^{2}+36m^{3}+9m^{4}$$

Expand

$$9m^{4}+36m^{3}+36m^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-6m-3m^{2}\right)^{2}.

$$36m^{2}+36mm^{2}+9\left(m^{2}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$36m^{2}+36m^{3}+9\left(m^{2}\right)^{2}$$

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

$$36m^{2}+36m^{3}+9m^{4}$$