Solve -4(x^2-1)^2+x^2

$$- 4 ( x ^ { 2 } - 1 ) ^ { 2 } + x ^ { 2 }$$

Evaluate

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

Solution Steps

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

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

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

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

Use the distributive property to multiply -4 by x^{4}-2x^{2}+1.

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

Combine 8x^{2} and x^{2} to get 9x^{2}.

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

Expand

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

Solution Steps

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

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

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

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

Use the distributive property to multiply -4 by x^{4}-2x^{2}+1.

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

Combine 8x^{2} and x^{2} to get 9x^{2}.

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