Solve (2m^2-7)^3=

$$( 2 m ^ { 2 } - 7 ) ^ { 3 } =$$

Evaluate

$$\left(2m^{2}-7\right)^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(2m^{2}-7\right)^{3}.

$$8\left(m^{2}\right)^{3}-84\left(m^{2}\right)^{2}+294m^{2}-343$$

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

$$8m^{6}-84\left(m^{2}\right)^{2}+294m^{2}-343$$

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

$$8m^{6}-84m^{4}+294m^{2}-343$$

Expand

$$8m^{6}-84m^{4}+294m^{2}-343$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(2m^{2}-7\right)^{3}.

$$8\left(m^{2}\right)^{3}-84\left(m^{2}\right)^{2}+294m^{2}-343$$

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

$$8m^{6}-84\left(m^{2}\right)^{2}+294m^{2}-343$$

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

$$8m^{6}-84m^{4}+294m^{2}-343$$