Solve (5x+6)(7x+12)(8x-4)(4x+3)

$$(5x+6)(7x+12)(8x-4)(4x+3)$$

Evaluate

$$1120x^{4}+3544x^{3}+2700x^{2}-648x-864$$

Solution Steps

Apply the distributive property by multiplying each term of 5x+6 by each term of 7x+12.

$$\left(35x^{2}+60x+42x+72\right)\left(8x-4\right)\left(4x+3\right)$$

Combine 60x and 42x to get 102x.

$$\left(35x^{2}+102x+72\right)\left(8x-4\right)\left(4x+3\right)$$

Apply the distributive property by multiplying each term of 35x^{2}+102x+72 by each term of 8x-4.

$$\left(280x^{3}-140x^{2}+816x^{2}-408x+576x-288\right)\left(4x+3\right)$$

Combine -140x^{2} and 816x^{2} to get 676x^{2}.

$$\left(280x^{3}+676x^{2}-408x+576x-288\right)\left(4x+3\right)$$

Combine -408x and 576x to get 168x.

$$\left(280x^{3}+676x^{2}+168x-288\right)\left(4x+3\right)$$

Apply the distributive property by multiplying each term of 280x^{3}+676x^{2}+168x-288 by each term of 4x+3.

$$1120x^{4}+840x^{3}+2704x^{3}+2028x^{2}+672x^{2}+504x-1152x-864$$

Combine 840x^{3} and 2704x^{3} to get 3544x^{3}.

$$1120x^{4}+3544x^{3}+2028x^{2}+672x^{2}+504x-1152x-864$$

Combine 2028x^{2} and 672x^{2} to get 2700x^{2}.

$$1120x^{4}+3544x^{3}+2700x^{2}+504x-1152x-864$$

Combine 504x and -1152x to get -648x.

$$1120x^{4}+3544x^{3}+2700x^{2}-648x-864$$

Expand

$$1120x^{4}+3544x^{3}+2700x^{2}-648x-864$$

Solution Steps

Apply the distributive property by multiplying each term of 5x+6 by each term of 7x+12.

$$\left(35x^{2}+60x+42x+72\right)\left(8x-4\right)\left(4x+3\right)$$

Combine 60x and 42x to get 102x.

$$\left(35x^{2}+102x+72\right)\left(8x-4\right)\left(4x+3\right)$$

Apply the distributive property by multiplying each term of 35x^{2}+102x+72 by each term of 8x-4.

$$\left(280x^{3}-140x^{2}+816x^{2}-408x+576x-288\right)\left(4x+3\right)$$

Combine -140x^{2} and 816x^{2} to get 676x^{2}.

$$\left(280x^{3}+676x^{2}-408x+576x-288\right)\left(4x+3\right)$$

Combine -408x and 576x to get 168x.

$$\left(280x^{3}+676x^{2}+168x-288\right)\left(4x+3\right)$$

Apply the distributive property by multiplying each term of 280x^{3}+676x^{2}+168x-288 by each term of 4x+3.

$$1120x^{4}+840x^{3}+2704x^{3}+2028x^{2}+672x^{2}+504x-1152x-864$$

Combine 840x^{3} and 2704x^{3} to get 3544x^{3}.

$$1120x^{4}+3544x^{3}+2028x^{2}+672x^{2}+504x-1152x-864$$

Combine 2028x^{2} and 672x^{2} to get 2700x^{2}.

$$1120x^{4}+3544x^{3}+2700x^{2}+504x-1152x-864$$

Combine 504x and -1152x to get -648x.

$$1120x^{4}+3544x^{3}+2700x^{2}-648x-864$$