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

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

Evaluate

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

Solution Steps

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

$$27\left(m^{2}\right)^{3}+54\left(m^{2}\right)^{2}m+36m^{2}m^{2}+8m^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$27m^{6}+54\left(m^{2}\right)^{2}m+36m^{2}m^{2}+8m^{3}$$

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

$$27m^{6}+54m^{4}m+36m^{2}m^{2}+8m^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$27m^{6}+54m^{5}+36m^{2}m^{2}+8m^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$27m^{6}+54m^{5}+36m^{4}+8m^{3}$$

Expand

$$27m^{6}+54m^{5}+36m^{4}+8m^{3}$$

Solution Steps

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

$$27\left(m^{2}\right)^{3}+54\left(m^{2}\right)^{2}m+36m^{2}m^{2}+8m^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$27m^{6}+54\left(m^{2}\right)^{2}m+36m^{2}m^{2}+8m^{3}$$

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

$$27m^{6}+54m^{4}m+36m^{2}m^{2}+8m^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$27m^{6}+54m^{5}+36m^{2}m^{2}+8m^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$27m^{6}+54m^{5}+36m^{4}+8m^{3}$$