Solve (x^2-10)^2-12(x^2-10)+32

$$( x ^ { 2 } - 10 ) ^ { 2 } - 12 ( x ^ { 2 } - 10 ) + 32$$

Evaluate

$$\left(x^{2}-18\right)\left(x^{2}-14\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{2}-10\right)^{2}.

$$\left(x^{2}\right)^{2}-20x^{2}+100-12\left(x^{2}-10\right)+32$$

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

$$x^{4}-20x^{2}+100-12\left(x^{2}-10\right)+32$$

Use the distributive property to multiply -12 by x^{2}-10.

$$x^{4}-20x^{2}+100-12x^{2}+120+32$$

Combine -20x^{2} and -12x^{2} to get -32x^{2}.

$$x^{4}-32x^{2}+100+120+32$$

Add 100 and 120 to get 220.

$$x^{4}-32x^{2}+220+32$$

Add 220 and 32 to get 252.

$$x^{4}-32x^{2}+252$$

Expand

$$x^{4}-32x^{2}+252$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{2}-10\right)^{2}.

$$\left(x^{2}\right)^{2}-20x^{2}+100-12\left(x^{2}-10\right)+32$$

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

$$x^{4}-20x^{2}+100-12\left(x^{2}-10\right)+32$$

Use the distributive property to multiply -12 by x^{2}-10.

$$x^{4}-20x^{2}+100-12x^{2}+120+32$$

Combine -20x^{2} and -12x^{2} to get -32x^{2}.

$$x^{4}-32x^{2}+100+120+32$$

Add 100 and 120 to get 220.

$$x^{4}-32x^{2}+220+32$$

Add 220 and 32 to get 252.

$$x^{4}-32x^{2}+252$$