Solve -55.125*left(x+4right)left(x+2right)left(x-1right)left(x-3right)

$$-55.125 \times \left( x+4 \right) \left( x+2 \right) \left( x-1 \right) \left( x-3 \right)$$

Evaluate

$$-\frac{441\left(x-3\right)\left(x-1\right)\left(x+2\right)\left(x+4\right)}{8}$$

Solution Steps

Use the distributive property to multiply -55.125 by x+4.

$$\left(-55.125x-220.5\right)\left(x+2\right)\left(x-1\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of -55.125x-220.5 by each term of x+2.

$$\left(-55.125x^{2}-110.25x-220.5x-441\right)\left(x-1\right)\left(x-3\right)$$

Combine -110.25x and -220.5x to get -330.75x.

$$\left(-55.125x^{2}-330.75x-441\right)\left(x-1\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of -55.125x^{2}-330.75x-441 by each term of x-1.

$$\left(-55.125x^{3}+55.125x^{2}-330.75x^{2}+330.75x-441x+441\right)\left(x-3\right)$$

Combine 55.125x^{2} and -330.75x^{2} to get -275.625x^{2}.

$$\left(-55.125x^{3}-275.625x^{2}+330.75x-441x+441\right)\left(x-3\right)$$

Combine 330.75x and -441x to get -110.25x.

$$\left(-55.125x^{3}-275.625x^{2}-110.25x+441\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of -55.125x^{3}-275.625x^{2}-110.25x+441 by each term of x-3.

$$-55.125x^{4}+165.375x^{3}-275.625x^{3}+826.875x^{2}-110.25x^{2}+330.75x+441x-1323$$

Combine 165.375x^{3} and -275.625x^{3} to get -110.25x^{3}.

$$-55.125x^{4}-110.25x^{3}+826.875x^{2}-110.25x^{2}+330.75x+441x-1323$$

Combine 826.875x^{2} and -110.25x^{2} to get 716.625x^{2}.

$$-55.125x^{4}-110.25x^{3}+716.625x^{2}+330.75x+441x-1323$$

Combine 330.75x and 441x to get 771.75x.

$$-55.125x^{4}-110.25x^{3}+716.625x^{2}+771.75x-1323$$

Expand

$$-\frac{441x^{4}}{8}-\frac{441x^{3}}{4}+\frac{5733x^{2}}{8}+\frac{3087x}{4}-1323$$

Solution Steps

Use the distributive property to multiply -55.125 by x+4.

$$\left(-55.125x-220.5\right)\left(x+2\right)\left(x-1\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of -55.125x-220.5 by each term of x+2.

$$\left(-55.125x^{2}-110.25x-220.5x-441\right)\left(x-1\right)\left(x-3\right)$$

Combine -110.25x and -220.5x to get -330.75x.

$$\left(-55.125x^{2}-330.75x-441\right)\left(x-1\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of -55.125x^{2}-330.75x-441 by each term of x-1.

$$\left(-55.125x^{3}+55.125x^{2}-330.75x^{2}+330.75x-441x+441\right)\left(x-3\right)$$

Combine 55.125x^{2} and -330.75x^{2} to get -275.625x^{2}.

$$\left(-55.125x^{3}-275.625x^{2}+330.75x-441x+441\right)\left(x-3\right)$$

Combine 330.75x and -441x to get -110.25x.

$$\left(-55.125x^{3}-275.625x^{2}-110.25x+441\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of -55.125x^{3}-275.625x^{2}-110.25x+441 by each term of x-3.

$$-55.125x^{4}+165.375x^{3}-275.625x^{3}+826.875x^{2}-110.25x^{2}+330.75x+441x-1323$$

Combine 165.375x^{3} and -275.625x^{3} to get -110.25x^{3}.

$$-55.125x^{4}-110.25x^{3}+826.875x^{2}-110.25x^{2}+330.75x+441x-1323$$

Combine 826.875x^{2} and -110.25x^{2} to get 716.625x^{2}.

$$-55.125x^{4}-110.25x^{3}+716.625x^{2}+330.75x+441x-1323$$

Combine 330.75x and 441x to get 771.75x.

$$-55.125x^{4}-110.25x^{3}+716.625x^{2}+771.75x-1323$$