Solve (x-4)*(3x+6)*(5-10x)*(12x+48)

$$( x - 4 ) \cdot ( 3 x + 6 ) \cdot ( 5 - 10 x ) \cdot ( 12 x + 48 )$$

Evaluate

$$180\left(1-2x\right)\left(x+2\right)\left(x^{2}-16\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x-4 by each term of 3x+6.

$$\left(3x^{2}+6x-12x-24\right)\left(5-10x\right)\left(12x+48\right)$$

Combine 6x and -12x to get -6x.

$$\left(3x^{2}-6x-24\right)\left(5-10x\right)\left(12x+48\right)$$

Apply the distributive property by multiplying each term of 3x^{2}-6x-24 by each term of 5-10x.

$$\left(15x^{2}-30x^{3}-30x+60x^{2}-120+240x\right)\left(12x+48\right)$$

Combine 15x^{2} and 60x^{2} to get 75x^{2}.

$$\left(75x^{2}-30x^{3}-30x-120+240x\right)\left(12x+48\right)$$

Combine -30x and 240x to get 210x.

$$\left(75x^{2}-30x^{3}+210x-120\right)\left(12x+48\right)$$

Apply the distributive property by multiplying each term of 75x^{2}-30x^{3}+210x-120 by each term of 12x+48.

$$900x^{3}+3600x^{2}-360x^{4}-1440x^{3}+2520x^{2}+10080x-1440x-5760$$

Combine 900x^{3} and -1440x^{3} to get -540x^{3}.

$$-540x^{3}+3600x^{2}-360x^{4}+2520x^{2}+10080x-1440x-5760$$

Combine 3600x^{2} and 2520x^{2} to get 6120x^{2}.

$$-540x^{3}+6120x^{2}-360x^{4}+10080x-1440x-5760$$

Combine 10080x and -1440x to get 8640x.

$$-540x^{3}+6120x^{2}-360x^{4}+8640x-5760$$

Expand

$$-360x^{4}-540x^{3}+6120x^{2}+8640x-5760$$

Solution Steps

Apply the distributive property by multiplying each term of x-4 by each term of 3x+6.

$$\left(3x^{2}+6x-12x-24\right)\left(5-10x\right)\left(12x+48\right)$$

Combine 6x and -12x to get -6x.

$$\left(3x^{2}-6x-24\right)\left(5-10x\right)\left(12x+48\right)$$

Apply the distributive property by multiplying each term of 3x^{2}-6x-24 by each term of 5-10x.

$$\left(15x^{2}-30x^{3}-30x+60x^{2}-120+240x\right)\left(12x+48\right)$$

Combine 15x^{2} and 60x^{2} to get 75x^{2}.

$$\left(75x^{2}-30x^{3}-30x-120+240x\right)\left(12x+48\right)$$

Combine -30x and 240x to get 210x.

$$\left(75x^{2}-30x^{3}+210x-120\right)\left(12x+48\right)$$

Apply the distributive property by multiplying each term of 75x^{2}-30x^{3}+210x-120 by each term of 12x+48.

$$900x^{3}+3600x^{2}-360x^{4}-1440x^{3}+2520x^{2}+10080x-1440x-5760$$

Combine 900x^{3} and -1440x^{3} to get -540x^{3}.

$$-540x^{3}+3600x^{2}-360x^{4}+2520x^{2}+10080x-1440x-5760$$

Combine 3600x^{2} and 2520x^{2} to get 6120x^{2}.

$$-540x^{3}+6120x^{2}-360x^{4}+10080x-1440x-5760$$

Combine 10080x and -1440x to get 8640x.

$$-540x^{3}+6120x^{2}-360x^{4}+8640x-5760$$