Solve (x^2-1)^2-6(x^2-1)+9

$$( x ^ { 2 } - 1 ) ^ { 2 } - 6 ( x ^ { 2 } - 1 ) + 9$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{2}-1\right)^{2}.

$$\left(x^{2}\right)^{2}-2x^{2}+1-6\left(x^{2}-1\right)+9$$

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

$$x^{4}-2x^{2}+1-6\left(x^{2}-1\right)+9$$

Use the distributive property to multiply -6 by x^{2}-1.

$$x^{4}-2x^{2}+1-6x^{2}+6+9$$

Combine -2x^{2} and -6x^{2} to get -8x^{2}.

$$x^{4}-8x^{2}+1+6+9$$

Add 1 and 6 to get 7.

$$x^{4}-8x^{2}+7+9$$

Add 7 and 9 to get 16.

$$x^{4}-8x^{2}+16$$

Expand

$$x^{4}-8x^{2}+16$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{2}-1\right)^{2}.

$$\left(x^{2}\right)^{2}-2x^{2}+1-6\left(x^{2}-1\right)+9$$

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

$$x^{4}-2x^{2}+1-6\left(x^{2}-1\right)+9$$

Use the distributive property to multiply -6 by x^{2}-1.

$$x^{4}-2x^{2}+1-6x^{2}+6+9$$

Combine -2x^{2} and -6x^{2} to get -8x^{2}.

$$x^{4}-8x^{2}+1+6+9$$

Add 1 and 6 to get 7.

$$x^{4}-8x^{2}+7+9$$

Add 7 and 9 to get 16.

$$x^{4}-8x^{2}+16$$