Solve 6x*(x-1)^2-3x*(x+1)^2

$$6 x \cdot ( x - 1 ) ^ { 2 } - 3 x \cdot ( x + 1 ) ^ { 2 }$$

Evaluate

$$3x\left(x^{2}-6x+1\right)$$

Solution Steps

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

$$6x\left(x^{2}-2x+1\right)-3x\left(x+1\right)^{2}$$

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

$$6x^{3}-12x^{2}+6x-3x\left(x+1\right)^{2}$$

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

$$6x^{3}-12x^{2}+6x-3x\left(x^{2}+2x+1\right)$$

Use the distributive property to multiply -3x by x^{2}+2x+1.

$$6x^{3}-12x^{2}+6x-3x^{3}-6x^{2}-3x$$

Combine 6x^{3} and -3x^{3} to get 3x^{3}.

$$3x^{3}-12x^{2}+6x-6x^{2}-3x$$

Combine -12x^{2} and -6x^{2} to get -18x^{2}.

$$3x^{3}-18x^{2}+6x-3x$$

Combine 6x and -3x to get 3x.

$$3x^{3}-18x^{2}+3x$$

Expand

$$3x^{3}-18x^{2}+3x$$

Solution Steps

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

$$6x\left(x^{2}-2x+1\right)-3x\left(x+1\right)^{2}$$

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

$$6x^{3}-12x^{2}+6x-3x\left(x+1\right)^{2}$$

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

$$6x^{3}-12x^{2}+6x-3x\left(x^{2}+2x+1\right)$$

Use the distributive property to multiply -3x by x^{2}+2x+1.

$$6x^{3}-12x^{2}+6x-3x^{3}-6x^{2}-3x$$

Combine 6x^{3} and -3x^{3} to get 3x^{3}.

$$3x^{3}-12x^{2}+6x-6x^{2}-3x$$

Combine -12x^{2} and -6x^{2} to get -18x^{2}.

$$3x^{3}-18x^{2}+6x-3x$$

Combine 6x and -3x to get 3x.

$$3x^{3}-18x^{2}+3x$$