Solve left(3x-2right)^2*(-2x+1)-3(6x^2-4x^2-3x-2)=

$${ \left(3x-2 \right) }^{ 2 } \times (-2x+1)-3(6 { x }^{ 2 } -4 { x }^{ 2 } -3x-2)=$$

Evaluate

$$10-11x+27x^{2}-18x^{3}$$

Solution Steps

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

$$\left(9x^{2}-12x+4\right)\left(-2x+1\right)-3\left(6x^{2}-4x^{2}-3x-2\right)$$

Use the distributive property to multiply 9x^{2}-12x+4 by -2x+1 and combine like terms.

$$-18x^{3}+33x^{2}-20x+4-3\left(6x^{2}-4x^{2}-3x-2\right)$$

Combine 6x^{2} and -4x^{2} to get 2x^{2}.

$$-18x^{3}+33x^{2}-20x+4-3\left(2x^{2}-3x-2\right)$$

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

$$-18x^{3}+33x^{2}-20x+4-6x^{2}+9x+6$$

Combine 33x^{2} and -6x^{2} to get 27x^{2}.

$$-18x^{3}+27x^{2}-20x+4+9x+6$$

Combine -20x and 9x to get -11x.

$$-18x^{3}+27x^{2}-11x+4+6$$

Add 4 and 6 to get 10.

$$-18x^{3}+27x^{2}-11x+10$$

Expand

$$10-11x+27x^{2}-18x^{3}$$

Solution Steps

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

$$\left(9x^{2}-12x+4\right)\left(-2x+1\right)-3\left(6x^{2}-4x^{2}-3x-2\right)$$

Use the distributive property to multiply 9x^{2}-12x+4 by -2x+1 and combine like terms.

$$-18x^{3}+33x^{2}-20x+4-3\left(6x^{2}-4x^{2}-3x-2\right)$$

Combine 6x^{2} and -4x^{2} to get 2x^{2}.

$$-18x^{3}+33x^{2}-20x+4-3\left(2x^{2}-3x-2\right)$$

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

$$-18x^{3}+33x^{2}-20x+4-6x^{2}+9x+6$$

Combine 33x^{2} and -6x^{2} to get 27x^{2}.

$$-18x^{3}+27x^{2}-20x+4+9x+6$$

Combine -20x and 9x to get -11x.

$$-18x^{3}+27x^{2}-11x+4+6$$

Add 4 and 6 to get 10.

$$-18x^{3}+27x^{2}-11x+10$$