Solve (3m^2+2m)^2

$$( 3 m ^ { 2 } + 2 m ) ^ { 2 }$$

Evaluate

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

Solution Steps

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

$$9\left(m^{2}\right)^{2}+12m^{2}m+4m^{2}$$

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

$$9m^{4}+12m^{2}m+4m^{2}$$

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

$$9m^{4}+12m^{3}+4m^{2}$$

Expand

$$9m^{4}+12m^{3}+4m^{2}$$

Solution Steps

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

$$9\left(m^{2}\right)^{2}+12m^{2}m+4m^{2}$$

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

$$9m^{4}+12m^{2}m+4m^{2}$$

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

$$9m^{4}+12m^{3}+4m^{2}$$