Solve left(x^2-9right)^2-x^2-6x-9

$${ \left( { x }^{ 2 } -9 \right) }^{ 2 } - { x }^{ 2 } -6x-9$$

Evaluate

$$\left(x-4\right)\left(x-2\right)\left(x+3\right)^{2}$$

Solution Steps

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

$$\left(x^{2}\right)^{2}-18x^{2}+81-x^{2}-6x-9$$

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

$$x^{4}-18x^{2}+81-x^{2}-6x-9$$

Combine -18x^{2} and -x^{2} to get -19x^{2}.

$$x^{4}-19x^{2}+81-6x-9$$

Subtract 9 from 81 to get 72.

$$x^{4}-19x^{2}+72-6x$$

Expand

$$x^{4}-19x^{2}-6x+72$$

Solution Steps

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

$$\left(x^{2}\right)^{2}-18x^{2}+81-x^{2}-6x-9$$

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

$$x^{4}-18x^{2}+81-x^{2}-6x-9$$

Combine -18x^{2} and -x^{2} to get -19x^{2}.

$$x^{4}-19x^{2}+81-6x-9$$

Subtract 9 from 81 to get 72.

$$x^{4}-19x^{2}+72-6x$$