Solve (4x-9)(x^2+x-12)-(2x+1)(2x^2-9+4)

$$(4x-9)( { x }^{ 2 } +x-12)-(2x+1)(2 { x }^{ 2 } -9+4)$$

Evaluate

$$113-47x-7x^{2}$$

Solution Steps

Use the distributive property to multiply 4x-9 by x^{2}+x-12 and combine like terms.

$$4x^{3}-5x^{2}-57x+108-\left(2x+1\right)\left(2x^{2}-9+4\right)$$

Add -9 and 4 to get -5.

$$4x^{3}-5x^{2}-57x+108-\left(2x+1\right)\left(2x^{2}-5\right)$$

Use the distributive property to multiply 2x+1 by 2x^{2}-5.

$$4x^{3}-5x^{2}-57x+108-\left(4x^{3}-10x+2x^{2}-5\right)$$

To find the opposite of 4x^{3}-10x+2x^{2}-5, find the opposite of each term.

$$4x^{3}-5x^{2}-57x+108-4x^{3}+10x-2x^{2}+5$$

Combine 4x^{3} and -4x^{3} to get 0.

$$-5x^{2}-57x+108+10x-2x^{2}+5$$

Combine -57x and 10x to get -47x.

$$-5x^{2}-47x+108-2x^{2}+5$$

Combine -5x^{2} and -2x^{2} to get -7x^{2}.

$$-7x^{2}-47x+108+5$$

Add 108 and 5 to get 113.

$$-7x^{2}-47x+113$$

Expand

$$113-47x-7x^{2}$$

Solution Steps

Use the distributive property to multiply 4x-9 by x^{2}+x-12 and combine like terms.

$$4x^{3}-5x^{2}-57x+108-\left(2x+1\right)\left(2x^{2}-9+4\right)$$

Add -9 and 4 to get -5.

$$4x^{3}-5x^{2}-57x+108-\left(2x+1\right)\left(2x^{2}-5\right)$$

Use the distributive property to multiply 2x+1 by 2x^{2}-5.

$$4x^{3}-5x^{2}-57x+108-\left(4x^{3}-10x+2x^{2}-5\right)$$

To find the opposite of 4x^{3}-10x+2x^{2}-5, find the opposite of each term.

$$4x^{3}-5x^{2}-57x+108-4x^{3}+10x-2x^{2}+5$$

Combine 4x^{3} and -4x^{3} to get 0.

$$-5x^{2}-57x+108+10x-2x^{2}+5$$

Combine -57x and 10x to get -47x.

$$-5x^{2}-47x+108-2x^{2}+5$$

Combine -5x^{2} and -2x^{2} to get -7x^{2}.

$$-7x^{2}-47x+108+5$$

Add 108 and 5 to get 113.

$$-7x^{2}-47x+113$$