Solve (9x+15)(12x+21)-(3x+5)(4x+7)

$$( 9 x + 15 ) ( 12 x + 21 ) - ( 3 x + 5 ) ( 4 x + 7 )$$

Evaluate

$$96x^{2}+328x+280$$

Solution Steps

Apply the distributive property by multiplying each term of 9x+15 by each term of 12x+21.

$$108x^{2}+189x+180x+315-\left(3x+5\right)\left(4x+7\right)$$

Combine 189x and 180x to get 369x.

$$108x^{2}+369x+315-\left(3x+5\right)\left(4x+7\right)$$

Apply the distributive property by multiplying each term of 3x+5 by each term of 4x+7.

$$108x^{2}+369x+315-\left(12x^{2}+21x+20x+35\right)$$

Combine 21x and 20x to get 41x.

$$108x^{2}+369x+315-\left(12x^{2}+41x+35\right)$$

To find the opposite of 12x^{2}+41x+35, find the opposite of each term.

$$108x^{2}+369x+315-12x^{2}-41x-35$$

Combine 108x^{2} and -12x^{2} to get 96x^{2}.

$$96x^{2}+369x+315-41x-35$$

Combine 369x and -41x to get 328x.

$$96x^{2}+328x+315-35$$

Subtract 35 from 315 to get 280.

$$96x^{2}+328x+280$$

Expand

$$96x^{2}+328x+280$$

Solution Steps

Apply the distributive property by multiplying each term of 9x+15 by each term of 12x+21.

$$108x^{2}+189x+180x+315-\left(3x+5\right)\left(4x+7\right)$$

Combine 189x and 180x to get 369x.

$$108x^{2}+369x+315-\left(3x+5\right)\left(4x+7\right)$$

Apply the distributive property by multiplying each term of 3x+5 by each term of 4x+7.

$$108x^{2}+369x+315-\left(12x^{2}+21x+20x+35\right)$$

Combine 21x and 20x to get 41x.

$$108x^{2}+369x+315-\left(12x^{2}+41x+35\right)$$

To find the opposite of 12x^{2}+41x+35, find the opposite of each term.

$$108x^{2}+369x+315-12x^{2}-41x-35$$

Combine 108x^{2} and -12x^{2} to get 96x^{2}.

$$96x^{2}+369x+315-41x-35$$

Combine 369x and -41x to get 328x.

$$96x^{2}+328x+315-35$$

Subtract 35 from 315 to get 280.

$$96x^{2}+328x+280$$