Solve (4x+1)(2x-3)-(8x-5)(x+3)

$$( 4 x + 1 ) ( 2 x - 3 ) - ( 8 x - 5 ) ( x + 3 )$$

Evaluate

$$12-29x$$

Solution Steps

Apply the distributive property by multiplying each term of 4x+1 by each term of 2x-3.

$$8x^{2}-12x+2x-3-\left(8x-5\right)\left(x+3\right)$$

Combine -12x and 2x to get -10x.

$$8x^{2}-10x-3-\left(8x-5\right)\left(x+3\right)$$

Apply the distributive property by multiplying each term of 8x-5 by each term of x+3.

$$8x^{2}-10x-3-\left(8x^{2}+24x-5x-15\right)$$

Combine 24x and -5x to get 19x.

$$8x^{2}-10x-3-\left(8x^{2}+19x-15\right)$$

To find the opposite of 8x^{2}+19x-15, find the opposite of each term.

$$8x^{2}-10x-3-8x^{2}-19x-\left(-15\right)$$

The opposite of -15 is 15.

$$8x^{2}-10x-3-8x^{2}-19x+15$$

Combine 8x^{2} and -8x^{2} to get 0.

$$-10x-3-19x+15$$

Combine -10x and -19x to get -29x.

$$-29x-3+15$$

Add -3 and 15 to get 12.

$$-29x+12$$

Expand

$$12-29x$$

Solution Steps

Apply the distributive property by multiplying each term of 4x+1 by each term of 2x-3.

$$8x^{2}-12x+2x-3-\left(8x-5\right)\left(x+3\right)$$

Combine -12x and 2x to get -10x.

$$8x^{2}-10x-3-\left(8x-5\right)\left(x+3\right)$$

Apply the distributive property by multiplying each term of 8x-5 by each term of x+3.

$$8x^{2}-10x-3-\left(8x^{2}+24x-5x-15\right)$$

Combine 24x and -5x to get 19x.

$$8x^{2}-10x-3-\left(8x^{2}+19x-15\right)$$

To find the opposite of 8x^{2}+19x-15, find the opposite of each term.

$$8x^{2}-10x-3-8x^{2}-19x-\left(-15\right)$$

The opposite of -15 is 15.

$$8x^{2}-10x-3-8x^{2}-19x+15$$

Combine 8x^{2} and -8x^{2} to get 0.

$$-10x-3-19x+15$$

Combine -10x and -19x to get -29x.

$$-29x-3+15$$

Add -3 and 15 to get 12.

$$-29x+12$$