Solve (x^2-6x)^2-12(x^2-6x)-64

$$( x ^ { 2 } - 6 x ) ^ { 2 } - 12 ( x ^ { 2 } - 6 x ) - 64$$

Evaluate

$$\left(x-8\right)\left(x+2\right)\left(x^{2}-6x+4\right)$$

Solution Steps

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

$$\left(x^{2}\right)^{2}-12x^{2}x+36x^{2}-12\left(x^{2}-6x\right)-64$$

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

$$x^{4}-12x^{2}x+36x^{2}-12\left(x^{2}-6x\right)-64$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$x^{4}-12x^{3}+36x^{2}-12\left(x^{2}-6x\right)-64$$

Use the distributive property to multiply -12 by x^{2}-6x.

$$x^{4}-12x^{3}+36x^{2}-12x^{2}+72x-64$$

Combine 36x^{2} and -12x^{2} to get 24x^{2}.

$$x^{4}-12x^{3}+24x^{2}+72x-64$$

Expand

$$x^{4}-12x^{3}+24x^{2}+72x-64$$

Solution Steps

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

$$\left(x^{2}\right)^{2}-12x^{2}x+36x^{2}-12\left(x^{2}-6x\right)-64$$

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

$$x^{4}-12x^{2}x+36x^{2}-12\left(x^{2}-6x\right)-64$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$x^{4}-12x^{3}+36x^{2}-12\left(x^{2}-6x\right)-64$$

Use the distributive property to multiply -12 by x^{2}-6x.

$$x^{4}-12x^{3}+36x^{2}-12x^{2}+72x-64$$

Combine 36x^{2} and -12x^{2} to get 24x^{2}.

$$x^{4}-12x^{3}+24x^{2}+72x-64$$