Solve (5+3m^2)^3

$$( 5 + 3 m ^ { 2 } ) ^ { 3 }$$

Evaluate

$$\left(3m^{2}+5\right)^{3}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(5+3m^{2}\right)^{3}.

$$125+225m^{2}+135\left(m^{2}\right)^{2}+27\left(m^{2}\right)^{3}$$

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

$$125+225m^{2}+135m^{4}+27\left(m^{2}\right)^{3}$$

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

$$125+225m^{2}+135m^{4}+27m^{6}$$

Expand

$$27m^{6}+135m^{4}+225m^{2}+125$$

Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(5+3m^{2}\right)^{3}.

$$125+225m^{2}+135\left(m^{2}\right)^{2}+27\left(m^{2}\right)^{3}$$

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

$$125+225m^{2}+135m^{4}+27\left(m^{2}\right)^{3}$$

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

$$125+225m^{2}+135m^{4}+27m^{6}$$