Solve A(x)=(3x+4)(2x-3)-(3x+4)(x-4)

$$A ( x ) = ( 3 x + 4 ) ( 2 x - 3 ) - ( 3 x + 4 ) ( x - 4 )$$

Evaluate

$$\left(x+1\right)\left(3x+4\right)$$

Solution Steps

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

$$6x^{2}-9x+8x-12-\left(3x+4\right)\left(x-4\right)$$

Combine -9x and 8x to get -x.

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

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

$$6x^{2}-x-12-\left(3x^{2}-12x+4x-16\right)$$

Combine -12x and 4x to get -8x.

$$6x^{2}-x-12-\left(3x^{2}-8x-16\right)$$

To find the opposite of 3x^{2}-8x-16, find the opposite of each term.

$$6x^{2}-x-12-3x^{2}-\left(-8x\right)-\left(-16\right)$$

The opposite of -8x is 8x.

$$6x^{2}-x-12-3x^{2}+8x-\left(-16\right)$$

The opposite of -16 is 16.

$$6x^{2}-x-12-3x^{2}+8x+16$$

Combine 6x^{2} and -3x^{2} to get 3x^{2}.

$$3x^{2}-x-12+8x+16$$

Combine -x and 8x to get 7x.

$$3x^{2}+7x-12+16$$

Add -12 and 16 to get 4.

$$3x^{2}+7x+4$$

Expand

$$3x^{2}+7x+4$$

Solution Steps

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

$$6x^{2}-9x+8x-12-\left(3x+4\right)\left(x-4\right)$$

Combine -9x and 8x to get -x.

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

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

$$6x^{2}-x-12-\left(3x^{2}-12x+4x-16\right)$$

Combine -12x and 4x to get -8x.

$$6x^{2}-x-12-\left(3x^{2}-8x-16\right)$$

To find the opposite of 3x^{2}-8x-16, find the opposite of each term.

$$6x^{2}-x-12-3x^{2}-\left(-8x\right)-\left(-16\right)$$

The opposite of -8x is 8x.

$$6x^{2}-x-12-3x^{2}+8x-\left(-16\right)$$

The opposite of -16 is 16.

$$6x^{2}-x-12-3x^{2}+8x+16$$

Combine 6x^{2} and -3x^{2} to get 3x^{2}.

$$3x^{2}-x-12+8x+16$$

Combine -x and 8x to get 7x.

$$3x^{2}+7x-12+16$$

Add -12 and 16 to get 4.

$$3x^{2}+7x+4$$