Solve (x+1)(x^2-x+1)3x(x+1)2(1-x)/(x-1)(x+1)(x+1)

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

Evaluate

$$-6x\left(x^{2}-x+1\right)$$

Solution Steps

Multiply x+1 and x+1 to get \left(x+1\right)^{2}.

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

Multiply x+1 and x+1 to get \left(x+1\right)^{2}.

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

Extract the negative sign in 1-x.

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

Cancel out \left(x-1\right)\left(x+1\right)^{2} in both numerator and denominator.

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

Multiply -2 and 3 to get -6.

$$-6x\left(x^{2}-x+1\right)$$

Use the distributive property to multiply -6x by x^{2}-x+1.

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

Expand

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

Solution Steps

Multiply x+1 and x+1 to get \left(x+1\right)^{2}.

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

Multiply x+1 and x+1 to get \left(x+1\right)^{2}.

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

Extract the negative sign in 1-x.

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

Cancel out \left(x-1\right)\left(x+1\right)^{2} in both numerator and denominator.

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

Multiply -2 and 3 to get -6.

$$-6x\left(x^{2}-x+1\right)$$

Use the distributive property to multiply -6x by x^{2}-x+1.

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