Solve (-5x-4)(-3x+6)-(-5x-4)(-2x+3)

$$( - 5 x - 4 ) ( - 3 x + 6 ) - ( - 5 x - 4 ) ( - 2 x + 3 )$$

Evaluate

$$5x^{2}-11x-12$$

Solution Steps

Apply the distributive property by multiplying each term of -5x-4 by each term of -3x+6.

$$15x^{2}-30x+12x-24-\left(-5x-4\right)\left(-2x+3\right)$$

Combine -30x and 12x to get -18x.

$$15x^{2}-18x-24-\left(-5x-4\right)\left(-2x+3\right)$$

Apply the distributive property by multiplying each term of -5x-4 by each term of -2x+3.

$$15x^{2}-18x-24-\left(10x^{2}-15x+8x-12\right)$$

Combine -15x and 8x to get -7x.

$$15x^{2}-18x-24-\left(10x^{2}-7x-12\right)$$

To find the opposite of 10x^{2}-7x-12, find the opposite of each term.

$$15x^{2}-18x-24-10x^{2}-\left(-7x\right)-\left(-12\right)$$

The opposite of -7x is 7x.

$$15x^{2}-18x-24-10x^{2}+7x-\left(-12\right)$$

The opposite of -12 is 12.

$$15x^{2}-18x-24-10x^{2}+7x+12$$

Combine 15x^{2} and -10x^{2} to get 5x^{2}.

$$5x^{2}-18x-24+7x+12$$

Combine -18x and 7x to get -11x.

$$5x^{2}-11x-24+12$$

Add -24 and 12 to get -12.

$$5x^{2}-11x-12$$

Expand

$$5x^{2}-11x-12$$

Solution Steps

Apply the distributive property by multiplying each term of -5x-4 by each term of -3x+6.

$$15x^{2}-30x+12x-24-\left(-5x-4\right)\left(-2x+3\right)$$

Combine -30x and 12x to get -18x.

$$15x^{2}-18x-24-\left(-5x-4\right)\left(-2x+3\right)$$

Apply the distributive property by multiplying each term of -5x-4 by each term of -2x+3.

$$15x^{2}-18x-24-\left(10x^{2}-15x+8x-12\right)$$

Combine -15x and 8x to get -7x.

$$15x^{2}-18x-24-\left(10x^{2}-7x-12\right)$$

To find the opposite of 10x^{2}-7x-12, find the opposite of each term.

$$15x^{2}-18x-24-10x^{2}-\left(-7x\right)-\left(-12\right)$$

The opposite of -7x is 7x.

$$15x^{2}-18x-24-10x^{2}+7x-\left(-12\right)$$

The opposite of -12 is 12.

$$15x^{2}-18x-24-10x^{2}+7x+12$$

Combine 15x^{2} and -10x^{2} to get 5x^{2}.

$$5x^{2}-18x-24+7x+12$$

Combine -18x and 7x to get -11x.

$$5x^{2}-11x-24+12$$

Add -24 and 12 to get -12.

$$5x^{2}-11x-12$$