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

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

Evaluate

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

Solution Steps

Multiply x^{2}-x and x^{2}-x to get \left(x^{2}-x\right)^{2}.

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

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

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

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

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

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

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

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

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

Expand

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

Solution Steps

Multiply x^{2}-x and x^{2}-x to get \left(x^{2}-x\right)^{2}.

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

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

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

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

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

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

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

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

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