Solve (6m^4+m)^3

$$( 6 m ^ { 4 } + m ) ^ { 3 }$$

Expand

$$216m^{12}+108m^{9}+18m^{6}+m^{3}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(6m^{4}+m\right)^{3}.

$$216\left(m^{4}\right)^{3}+108\left(m^{4}\right)^{2}m+18m^{4}m^{2}+m^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$216m^{12}+108\left(m^{4}\right)^{2}m+18m^{4}m^{2}+m^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$216m^{12}+108m^{8}m+18m^{4}m^{2}+m^{3}$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$216m^{12}+108m^{9}+18m^{4}m^{2}+m^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$216m^{12}+108m^{9}+18m^{6}+m^{3}$$

Evaluate

$$\left(6m^{4}+m\right)^{3}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(6m^{4}+m\right)^{3}.

$$216\left(m^{4}\right)^{3}+108\left(m^{4}\right)^{2}m+18m^{4}m^{2}+m^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$216m^{12}+108\left(m^{4}\right)^{2}m+18m^{4}m^{2}+m^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$216m^{12}+108m^{8}m+18m^{4}m^{2}+m^{3}$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$216m^{12}+108m^{9}+18m^{4}m^{2}+m^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$216m^{12}+108m^{9}+18m^{6}+m^{3}$$