Solve (x^2-3)^2-4x^2

$$( x ^ { 2 } - 3 ) ^ { 2 } - 4 x ^ { 2 }$$

Evaluate

$$x^{4}-10x^{2}+9$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{2}-3\right)^{2}.

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

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

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

Combine -6x^{2} and -4x^{2} to get -10x^{2}.

$$x^{4}-10x^{2}+9$$

Expand

$$x^{4}-10x^{2}+9$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{2}-3\right)^{2}.

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

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

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

Combine -6x^{2} and -4x^{2} to get -10x^{2}.

$$x^{4}-10x^{2}+9$$