Solve left(3x-6right)left(x^2-1right)-left(5x-10right)left(x-1right)^2

$$\left( 3x-6 \right) \left( { x }^{ 2 } -1 \right) - \left( 5x-10 \right) { \left( x-1 \right) }^{ 2 }$$

Evaluate

$$2\left(4-x\right)\left(x-2\right)\left(x-1\right)$$

Solution Steps

Use the distributive property to multiply 3x-6 by x^{2}-1.

$$3x^{3}-3x-6x^{2}+6-\left(5x-10\right)\left(x-1\right)^{2}$$

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

$$3x^{3}-3x-6x^{2}+6-\left(5x-10\right)\left(x^{2}-2x+1\right)$$

Use the distributive property to multiply 5x-10 by x^{2}-2x+1 and combine like terms.

$$3x^{3}-3x-6x^{2}+6-\left(5x^{3}-20x^{2}+25x-10\right)$$

To find the opposite of 5x^{3}-20x^{2}+25x-10, find the opposite of each term.

$$3x^{3}-3x-6x^{2}+6-5x^{3}+20x^{2}-25x+10$$

Combine 3x^{3} and -5x^{3} to get -2x^{3}.

$$-2x^{3}-3x-6x^{2}+6+20x^{2}-25x+10$$

Combine -6x^{2} and 20x^{2} to get 14x^{2}.

$$-2x^{3}-3x+14x^{2}+6-25x+10$$

Combine -3x and -25x to get -28x.

$$-2x^{3}-28x+14x^{2}+6+10$$

Add 6 and 10 to get 16.

$$-2x^{3}-28x+14x^{2}+16$$

Expand

$$16-28x+14x^{2}-2x^{3}$$

Solution Steps

Use the distributive property to multiply 3x-6 by x^{2}-1.

$$3x^{3}-3x-6x^{2}+6-\left(5x-10\right)\left(x-1\right)^{2}$$

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

$$3x^{3}-3x-6x^{2}+6-\left(5x-10\right)\left(x^{2}-2x+1\right)$$

Use the distributive property to multiply 5x-10 by x^{2}-2x+1 and combine like terms.

$$3x^{3}-3x-6x^{2}+6-\left(5x^{3}-20x^{2}+25x-10\right)$$

To find the opposite of 5x^{3}-20x^{2}+25x-10, find the opposite of each term.

$$3x^{3}-3x-6x^{2}+6-5x^{3}+20x^{2}-25x+10$$

Combine 3x^{3} and -5x^{3} to get -2x^{3}.

$$-2x^{3}-3x-6x^{2}+6+20x^{2}-25x+10$$

Combine -6x^{2} and 20x^{2} to get 14x^{2}.

$$-2x^{3}-3x+14x^{2}+6-25x+10$$

Combine -3x and -25x to get -28x.

$$-2x^{3}-28x+14x^{2}+6+10$$

Add 6 and 10 to get 16.

$$-2x^{3}-28x+14x^{2}+16$$