Solve (6x^2-72)^2

$$( 6 x ^ { 2 } - 72 ) ^ { 2 }$$

Evaluate

$$36\left(x^{2}-12\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6x^{2}-72\right)^{2}.

$$36\left(x^{2}\right)^{2}-864x^{2}+5184$$

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

$$36x^{4}-864x^{2}+5184$$

Expand

$$36x^{4}-864x^{2}+5184$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6x^{2}-72\right)^{2}.

$$36\left(x^{2}\right)^{2}-864x^{2}+5184$$

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

$$36x^{4}-864x^{2}+5184$$