Solve (x^2+7)^3

$$( x ^ { 2 } + 7 ) ^ { 3 }$$

Expand

$$x^{6}+21x^{4}+147x^{2}+343$$

Solution Steps

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

$$\left(x^{2}\right)^{3}+21\left(x^{2}\right)^{2}+147x^{2}+343$$

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

$$x^{6}+21\left(x^{2}\right)^{2}+147x^{2}+343$$

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

$$x^{6}+21x^{4}+147x^{2}+343$$

Evaluate

$$\left(x^{2}+7\right)^{3}$$

Solution Steps

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

$$\left(x^{2}\right)^{3}+21\left(x^{2}\right)^{2}+147x^{2}+343$$

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

$$x^{6}+21\left(x^{2}\right)^{2}+147x^{2}+343$$

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

$$x^{6}+21x^{4}+147x^{2}+343$$