Solve W(x)=x^3(x^2-7)^2-36x

$$W ( x ) = x ^ { 3 } ( x ^ { 2 } - 7 ) ^ { 2 } - 36 x$$

Evaluate

$$x\left(\left(x\left(x^{2}-7\right)\right)^{2}-36\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{2}-7\right)^{2}.

$$x^{3}\left(\left(x^{2}\right)^{2}-14x^{2}+49\right)-36x$$

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

$$x^{3}\left(x^{4}-14x^{2}+49\right)-36x$$

Use the distributive property to multiply x^{3} by x^{4}-14x^{2}+49.

$$x^{7}-14x^{5}+49x^{3}-36x$$

Expand

$$x^{7}-14x^{5}+49x^{3}-36x$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{2}-7\right)^{2}.

$$x^{3}\left(\left(x^{2}\right)^{2}-14x^{2}+49\right)-36x$$

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

$$x^{3}\left(x^{4}-14x^{2}+49\right)-36x$$

Use the distributive property to multiply x^{3} by x^{4}-14x^{2}+49.

$$x^{7}-14x^{5}+49x^{3}-36x$$