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

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

Evaluate

$$-\frac{12x\left(x^{2}+3x+1\right)}{5}$$

Solution Steps

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

$$0.6x\left(x^{2}-2x+1\right)-3x\left(x+1\right)^{2}$$

Use the distributive property to multiply 0.6x by x^{2}-2x+1.

$$0.6x^{3}-1.2x^{2}+0.6x-3x\left(x+1\right)^{2}$$

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

$$0.6x^{3}-1.2x^{2}+0.6x-3x\left(x^{2}+2x+1\right)$$

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

$$0.6x^{3}-1.2x^{2}+0.6x-3x^{3}-6x^{2}-3x$$

Combine 0.6x^{3} and -3x^{3} to get -2.4x^{3}.

$$-2.4x^{3}-1.2x^{2}+0.6x-6x^{2}-3x$$

Combine -1.2x^{2} and -6x^{2} to get -7.2x^{2}.

$$-2.4x^{3}-7.2x^{2}+0.6x-3x$$

Combine 0.6x and -3x to get -2.4x.

$$-2.4x^{3}-7.2x^{2}-2.4x$$

Expand

$$\frac{-12x^{3}-36x^{2}-12x}{5}$$

Solution Steps

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

$$0.6x\left(x^{2}-2x+1\right)-3x\left(x+1\right)^{2}$$

Use the distributive property to multiply 0.6x by x^{2}-2x+1.

$$0.6x^{3}-1.2x^{2}+0.6x-3x\left(x+1\right)^{2}$$

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

$$0.6x^{3}-1.2x^{2}+0.6x-3x\left(x^{2}+2x+1\right)$$

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

$$0.6x^{3}-1.2x^{2}+0.6x-3x^{3}-6x^{2}-3x$$

Combine 0.6x^{3} and -3x^{3} to get -2.4x^{3}.

$$-2.4x^{3}-1.2x^{2}+0.6x-6x^{2}-3x$$

Combine -1.2x^{2} and -6x^{2} to get -7.2x^{2}.

$$-2.4x^{3}-7.2x^{2}+0.6x-3x$$

Combine 0.6x and -3x to get -2.4x.

$$-2.4x^{3}-7.2x^{2}-2.4x$$