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

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

Evaluate

$$12\left(x^{2}-1\right)$$

Solution Steps

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

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

Combine 4x and -9x to get -5x.

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

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

$$6x^{2}-5x-6-\left(4x-6x^{2}+6-9x\right)$$

Combine 4x and -9x to get -5x.

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

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

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

The opposite of -5x is 5x.

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

The opposite of -6x^{2} is 6x^{2}.

$$6x^{2}-5x-6+5x+6x^{2}-6$$

Combine -5x and 5x to get 0.

$$6x^{2}-6+6x^{2}-6$$

Combine 6x^{2} and 6x^{2} to get 12x^{2}.

$$12x^{2}-6-6$$

Subtract 6 from -6 to get -12.

$$12x^{2}-12$$

Expand

$$12x^{2}-12$$

Solution Steps

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

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

Combine 4x and -9x to get -5x.

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

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

$$6x^{2}-5x-6-\left(4x-6x^{2}+6-9x\right)$$

Combine 4x and -9x to get -5x.

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

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

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

The opposite of -5x is 5x.

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

The opposite of -6x^{2} is 6x^{2}.

$$6x^{2}-5x-6+5x+6x^{2}-6$$

Combine -5x and 5x to get 0.

$$6x^{2}-6+6x^{2}-6$$

Combine 6x^{2} and 6x^{2} to get 12x^{2}.

$$12x^{2}-6-6$$

Subtract 6 from -6 to get -12.

$$12x^{2}-12$$