Solve (x^2-9)^2x

$$( x ^ { 2 } - 9 ) ^ { 2 } x$$

Evaluate

$$x\left(x^{2}-9\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{2}-9\right)^{2}.

$$\left(\left(x^{2}\right)^{2}-18x^{2}+81\right)x$$

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

$$\left(x^{4}-18x^{2}+81\right)x$$

Use the distributive property to multiply x^{4}-18x^{2}+81 by x.

$$x^{5}-18x^{3}+81x$$

Expand

$$x^{5}-18x^{3}+81x$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{2}-9\right)^{2}.

$$\left(\left(x^{2}\right)^{2}-18x^{2}+81\right)x$$

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

$$\left(x^{4}-18x^{2}+81\right)x$$

Use the distributive property to multiply x^{4}-18x^{2}+81 by x.

$$x^{5}-18x^{3}+81x$$