Solve =2x(3x)+2x(-4)-1(3x)-1(4)-(2x-3)^2

$$= 2 x ( 3 x ) + 2 x ( - 4 ) - 1 ( 3 x ) - 1 ( 4 ) - ( 2 x - 3 ) ^ { 2 }$$

Evaluate

$$2x^{2}+x-13$$

Solution Steps

Multiply x and x to get x^{2}.

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

Multiply 2 and 3 to get 6.

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

Multiply 2 and -4 to get -8.

$$6x^{2}-8x-1\times 3x-1\times 4-\left(2x-3\right)^{2}$$

Multiply 1 and 3 to get 3.

$$6x^{2}-8x-3x-1\times 4-\left(2x-3\right)^{2}$$

Combine -8x and -3x to get -11x.

$$6x^{2}-11x-1\times 4-\left(2x-3\right)^{2}$$

Multiply 1 and 4 to get 4.

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

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

$$6x^{2}-11x-4-\left(4x^{2}-12x+9\right)$$

To find the opposite of 4x^{2}-12x+9, find the opposite of each term.

$$6x^{2}-11x-4-4x^{2}+12x-9$$

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

$$2x^{2}-11x-4+12x-9$$

Combine -11x and 12x to get x.

$$2x^{2}+x-4-9$$

Subtract 9 from -4 to get -13.

$$2x^{2}+x-13$$

Expand

$$2x^{2}+x-13$$

Solution Steps

Multiply x and x to get x^{2}.

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

Multiply 2 and 3 to get 6.

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

Multiply 2 and -4 to get -8.

$$6x^{2}-8x-1\times 3x-1\times 4-\left(2x-3\right)^{2}$$

Multiply 1 and 3 to get 3.

$$6x^{2}-8x-3x-1\times 4-\left(2x-3\right)^{2}$$

Combine -8x and -3x to get -11x.

$$6x^{2}-11x-1\times 4-\left(2x-3\right)^{2}$$

Multiply 1 and 4 to get 4.

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

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

$$6x^{2}-11x-4-\left(4x^{2}-12x+9\right)$$

To find the opposite of 4x^{2}-12x+9, find the opposite of each term.

$$6x^{2}-11x-4-4x^{2}+12x-9$$

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

$$2x^{2}-11x-4+12x-9$$

Combine -11x and 12x to get x.

$$2x^{2}+x-4-9$$

Subtract 9 from -4 to get -13.

$$2x^{2}+x-13$$