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

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

Evaluate

$$x^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-1\right)^{3}.

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

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

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

Combine -3x^{2} and x^{2} to get -2x^{2}.

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

Combine 3x and -2x to get x.

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

Add -1 and 1 to get 0.

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

Use the distributive property to multiply x by 2x-1.

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

Combine -2x^{2} and 2x^{2} to get 0.

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

Combine x and -x to get 0.

$$x^{3}$$

Expand

$$x^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-1\right)^{3}.

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

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

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

Combine -3x^{2} and x^{2} to get -2x^{2}.

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

Combine 3x and -2x to get x.

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

Add -1 and 1 to get 0.

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

Use the distributive property to multiply x by 2x-1.

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

Combine -2x^{2} and 2x^{2} to get 0.

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

Combine x and -x to get 0.

$$x^{3}$$