Solve (-3x+4)(3x-8)-(-3x+4)(7x+2)

$$( - 3 x + 4 ) ( 3 x - 8 ) - ( - 3 x + 4 ) ( 7 x + 2 )$$

Evaluate

$$12x^{2}+14x-40$$

Solution Steps

Apply the distributive property by multiplying each term of -3x+4 by each term of 3x-8.

$$-9x^{2}+24x+12x-32-\left(-3x+4\right)\left(7x+2\right)$$

Combine 24x and 12x to get 36x.

$$-9x^{2}+36x-32-\left(-3x+4\right)\left(7x+2\right)$$

Apply the distributive property by multiplying each term of -3x+4 by each term of 7x+2.

$$-9x^{2}+36x-32-\left(-21x^{2}-6x+28x+8\right)$$

Combine -6x and 28x to get 22x.

$$-9x^{2}+36x-32-\left(-21x^{2}+22x+8\right)$$

To find the opposite of -21x^{2}+22x+8, find the opposite of each term.

$$-9x^{2}+36x-32-\left(-21x^{2}\right)-22x-8$$

The opposite of -21x^{2} is 21x^{2}.

$$-9x^{2}+36x-32+21x^{2}-22x-8$$

Combine -9x^{2} and 21x^{2} to get 12x^{2}.

$$12x^{2}+36x-32-22x-8$$

Combine 36x and -22x to get 14x.

$$12x^{2}+14x-32-8$$

Subtract 8 from -32 to get -40.

$$12x^{2}+14x-40$$

Expand

$$12x^{2}+14x-40$$

Solution Steps

Apply the distributive property by multiplying each term of -3x+4 by each term of 3x-8.

$$-9x^{2}+24x+12x-32-\left(-3x+4\right)\left(7x+2\right)$$

Combine 24x and 12x to get 36x.

$$-9x^{2}+36x-32-\left(-3x+4\right)\left(7x+2\right)$$

Apply the distributive property by multiplying each term of -3x+4 by each term of 7x+2.

$$-9x^{2}+36x-32-\left(-21x^{2}-6x+28x+8\right)$$

Combine -6x and 28x to get 22x.

$$-9x^{2}+36x-32-\left(-21x^{2}+22x+8\right)$$

To find the opposite of -21x^{2}+22x+8, find the opposite of each term.

$$-9x^{2}+36x-32-\left(-21x^{2}\right)-22x-8$$

The opposite of -21x^{2} is 21x^{2}.

$$-9x^{2}+36x-32+21x^{2}-22x-8$$

Combine -9x^{2} and 21x^{2} to get 12x^{2}.

$$12x^{2}+36x-32-22x-8$$

Combine 36x and -22x to get 14x.

$$12x^{2}+14x-32-8$$

Subtract 8 from -32 to get -40.

$$12x^{2}+14x-40$$