Solve (x^2-7x)^2+6x^2-42x

$$( x ^ { 2 } - 7 x ) ^ { 2 } + 6 x ^ { 2 } - 42 x$$

Evaluate

$$x\left(x-7\right)\left(x-6\right)\left(x-1\right)$$

Solution Steps

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

$$\left(x^{2}\right)^{2}-14x^{2}x+49x^{2}+6x^{2}-42x$$

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

$$x^{4}-14x^{2}x+49x^{2}+6x^{2}-42x$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$x^{4}-14x^{3}+49x^{2}+6x^{2}-42x$$

Combine 49x^{2} and 6x^{2} to get 55x^{2}.

$$x^{4}-14x^{3}+55x^{2}-42x$$

Expand

$$x^{4}-14x^{3}+55x^{2}-42x$$

Solution Steps

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

$$\left(x^{2}\right)^{2}-14x^{2}x+49x^{2}+6x^{2}-42x$$

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

$$x^{4}-14x^{2}x+49x^{2}+6x^{2}-42x$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$x^{4}-14x^{3}+49x^{2}+6x^{2}-42x$$

Combine 49x^{2} and 6x^{2} to get 55x^{2}.

$$x^{4}-14x^{3}+55x^{2}-42x$$