Solve (x^2-1)^2-11*(x^2-1)+24

$$( x ^ { 2 } - 1 ) ^ { 2 } - 11 \cdot ( x ^ { 2 } - 1 ) + 24$$

Evaluate

$$x^{4}-13x^{2}+36$$

Solution Steps

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

$$\left(x^{2}\right)^{2}-2x^{2}+1-11\left(x^{2}-1\right)+24$$

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

$$x^{4}-2x^{2}+1-11\left(x^{2}-1\right)+24$$

Use the distributive property to multiply -11 by x^{2}-1.

$$x^{4}-2x^{2}+1-11x^{2}+11+24$$

Combine -2x^{2} and -11x^{2} to get -13x^{2}.

$$x^{4}-13x^{2}+1+11+24$$

Add 1 and 11 to get 12.

$$x^{4}-13x^{2}+12+24$$

Add 12 and 24 to get 36.

$$x^{4}-13x^{2}+36$$

Expand

$$x^{4}-13x^{2}+36$$

Solution Steps

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

$$\left(x^{2}\right)^{2}-2x^{2}+1-11\left(x^{2}-1\right)+24$$

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

$$x^{4}-2x^{2}+1-11\left(x^{2}-1\right)+24$$

Use the distributive property to multiply -11 by x^{2}-1.

$$x^{4}-2x^{2}+1-11x^{2}+11+24$$

Combine -2x^{2} and -11x^{2} to get -13x^{2}.

$$x^{4}-13x^{2}+1+11+24$$

Add 1 and 11 to get 12.

$$x^{4}-13x^{2}+12+24$$

Add 12 and 24 to get 36.

$$x^{4}-13x^{2}+36$$