Solve 3(2x+1)(2x-1)-2(3x+2)(2-3x)

$$3 ( 2 x + 1 ) ( 2 x - 1 ) - 2 ( 3 x + 2 ) ( 2 - 3 x )$$

Evaluate

$$30x^{2}-11$$

Solution Steps

Use the distributive property to multiply 3 by 2x+1.

$$\left(6x+3\right)\left(2x-1\right)-2\left(3x+2\right)\left(2-3x\right)$$

Apply the distributive property by multiplying each term of 6x+3 by each term of 2x-1.

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

Combine -6x and 6x to get 0.

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

Use the distributive property to multiply -2 by 3x+2.

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

Apply the distributive property by multiplying each term of -6x-4 by each term of 2-3x.

$$12x^{2}-3-12x+18x^{2}-8+12x$$

Combine -12x and 12x to get 0.

$$12x^{2}-3+18x^{2}-8$$

Combine 12x^{2} and 18x^{2} to get 30x^{2}.

$$30x^{2}-3-8$$

Subtract 8 from -3 to get -11.

$$30x^{2}-11$$

Expand

$$30x^{2}-11$$

Solution Steps

Use the distributive property to multiply 3 by 2x+1.

$$\left(6x+3\right)\left(2x-1\right)-2\left(3x+2\right)\left(2-3x\right)$$

Apply the distributive property by multiplying each term of 6x+3 by each term of 2x-1.

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

Combine -6x and 6x to get 0.

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

Use the distributive property to multiply -2 by 3x+2.

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

Apply the distributive property by multiplying each term of -6x-4 by each term of 2-3x.

$$12x^{2}-3-12x+18x^{2}-8+12x$$

Combine -12x and 12x to get 0.

$$12x^{2}-3+18x^{2}-8$$

Combine 12x^{2} and 18x^{2} to get 30x^{2}.

$$30x^{2}-3-8$$

Subtract 8 from -3 to get -11.

$$30x^{2}-11$$