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

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

Evaluate

$$\left(x-3\right)\left(x+1\right)\left(x^{2}+x-3\right)$$

Solution Steps

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

$$\left(x^{2}\right)^{2}-6x^{2}+9-x\left(x^{2}-3\right)-2x^{2}$$

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

$$x^{4}-6x^{2}+9-x\left(x^{2}-3\right)-2x^{2}$$

Use the distributive property to multiply x by x^{2}-3.

$$x^{4}-6x^{2}+9-\left(x^{3}-3x\right)-2x^{2}$$

To find the opposite of x^{3}-3x, find the opposite of each term.

$$x^{4}-6x^{2}+9-x^{3}+3x-2x^{2}$$

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

$$x^{4}-8x^{2}+9-x^{3}+3x$$

Expand

$$x^{4}-x^{3}-8x^{2}+3x+9$$

Solution Steps

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

$$\left(x^{2}\right)^{2}-6x^{2}+9-x\left(x^{2}-3\right)-2x^{2}$$

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

$$x^{4}-6x^{2}+9-x\left(x^{2}-3\right)-2x^{2}$$

Use the distributive property to multiply x by x^{2}-3.

$$x^{4}-6x^{2}+9-\left(x^{3}-3x\right)-2x^{2}$$

To find the opposite of x^{3}-3x, find the opposite of each term.

$$x^{4}-6x^{2}+9-x^{3}+3x-2x^{2}$$

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

$$x^{4}-8x^{2}+9-x^{3}+3x$$