Solve left(3x-4right)left(2x^2-5x+1right)-left(2x-1right)left(3x^2+7x-5right)

$$\left( 3x-4 \right) \left( 2 { x }^{ 2 } -5x+1 \right) - \left( 2x-1 \right) \left( 3 { x }^{ 2 } +7x-5 \right)$$

Evaluate

$$-34x^{2}+40x-9$$

Solution Steps

Use the distributive property to multiply 3x-4 by 2x^{2}-5x+1 and combine like terms.

$$6x^{3}-23x^{2}+23x-4-\left(2x-1\right)\left(3x^{2}+7x-5\right)$$

Use the distributive property to multiply 2x-1 by 3x^{2}+7x-5 and combine like terms.

$$6x^{3}-23x^{2}+23x-4-\left(6x^{3}+11x^{2}-17x+5\right)$$

To find the opposite of 6x^{3}+11x^{2}-17x+5, find the opposite of each term.

$$6x^{3}-23x^{2}+23x-4-6x^{3}-11x^{2}+17x-5$$

Combine 6x^{3} and -6x^{3} to get 0.

$$-23x^{2}+23x-4-11x^{2}+17x-5$$

Combine -23x^{2} and -11x^{2} to get -34x^{2}.

$$-34x^{2}+23x-4+17x-5$$

Combine 23x and 17x to get 40x.

$$-34x^{2}+40x-4-5$$

Subtract 5 from -4 to get -9.

$$-34x^{2}+40x-9$$

Expand

$$-34x^{2}+40x-9$$

Solution Steps

Use the distributive property to multiply 3x-4 by 2x^{2}-5x+1 and combine like terms.

$$6x^{3}-23x^{2}+23x-4-\left(2x-1\right)\left(3x^{2}+7x-5\right)$$

Use the distributive property to multiply 2x-1 by 3x^{2}+7x-5 and combine like terms.

$$6x^{3}-23x^{2}+23x-4-\left(6x^{3}+11x^{2}-17x+5\right)$$

To find the opposite of 6x^{3}+11x^{2}-17x+5, find the opposite of each term.

$$6x^{3}-23x^{2}+23x-4-6x^{3}-11x^{2}+17x-5$$

Combine 6x^{3} and -6x^{3} to get 0.

$$-23x^{2}+23x-4-11x^{2}+17x-5$$

Combine -23x^{2} and -11x^{2} to get -34x^{2}.

$$-34x^{2}+23x-4+17x-5$$

Combine 23x and 17x to get 40x.

$$-34x^{2}+40x-4-5$$

Subtract 5 from -4 to get -9.

$$-34x^{2}+40x-9$$