Solve (3x+9)(3x-4)-(2x+5)(2x-9)

$$( 3 x + 9 ) ( 3 x - 4 ) - ( 2 x + 5 ) ( 2 x - 9 )$$

Evaluate

$$5x^{2}+23x+9$$

Solution Steps

Apply the distributive property by multiplying each term of 3x+9 by each term of 3x-4.

$$9x^{2}-12x+27x-36-\left(2x+5\right)\left(2x-9\right)$$

Combine -12x and 27x to get 15x.

$$9x^{2}+15x-36-\left(2x+5\right)\left(2x-9\right)$$

Apply the distributive property by multiplying each term of 2x+5 by each term of 2x-9.

$$9x^{2}+15x-36-\left(4x^{2}-18x+10x-45\right)$$

Combine -18x and 10x to get -8x.

$$9x^{2}+15x-36-\left(4x^{2}-8x-45\right)$$

To find the opposite of 4x^{2}-8x-45, find the opposite of each term.

$$9x^{2}+15x-36-4x^{2}-\left(-8x\right)-\left(-45\right)$$

The opposite of -8x is 8x.

$$9x^{2}+15x-36-4x^{2}+8x-\left(-45\right)$$

The opposite of -45 is 45.

$$9x^{2}+15x-36-4x^{2}+8x+45$$

Combine 9x^{2} and -4x^{2} to get 5x^{2}.

$$5x^{2}+15x-36+8x+45$$

Combine 15x and 8x to get 23x.

$$5x^{2}+23x-36+45$$

Add -36 and 45 to get 9.

$$5x^{2}+23x+9$$

Expand

$$5x^{2}+23x+9$$

Solution Steps

Apply the distributive property by multiplying each term of 3x+9 by each term of 3x-4.

$$9x^{2}-12x+27x-36-\left(2x+5\right)\left(2x-9\right)$$

Combine -12x and 27x to get 15x.

$$9x^{2}+15x-36-\left(2x+5\right)\left(2x-9\right)$$

Apply the distributive property by multiplying each term of 2x+5 by each term of 2x-9.

$$9x^{2}+15x-36-\left(4x^{2}-18x+10x-45\right)$$

Combine -18x and 10x to get -8x.

$$9x^{2}+15x-36-\left(4x^{2}-8x-45\right)$$

To find the opposite of 4x^{2}-8x-45, find the opposite of each term.

$$9x^{2}+15x-36-4x^{2}-\left(-8x\right)-\left(-45\right)$$

The opposite of -8x is 8x.

$$9x^{2}+15x-36-4x^{2}+8x-\left(-45\right)$$

The opposite of -45 is 45.

$$9x^{2}+15x-36-4x^{2}+8x+45$$

Combine 9x^{2} and -4x^{2} to get 5x^{2}.

$$5x^{2}+15x-36+8x+45$$

Combine 15x and 8x to get 23x.

$$5x^{2}+23x-36+45$$

Add -36 and 45 to get 9.

$$5x^{2}+23x+9$$