Solve (x+53)(x+55)(x+57)(x+5)

$$( x + 53 ) ( x + 55 ) ( x + 57 ) ( x + 5 )$$

Evaluate

$$\left(x+5\right)\left(x+53\right)\left(x+55\right)\left(x+57\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x+53 by each term of x+55.

$$\left(x^{2}+55x+53x+2915\right)\left(x+57\right)\left(x+5\right)$$

Combine 55x and 53x to get 108x.

$$\left(x^{2}+108x+2915\right)\left(x+57\right)\left(x+5\right)$$

Apply the distributive property by multiplying each term of x^{2}+108x+2915 by each term of x+57.

$$\left(x^{3}+57x^{2}+108x^{2}+6156x+2915x+166155\right)\left(x+5\right)$$

Combine 57x^{2} and 108x^{2} to get 165x^{2}.

$$\left(x^{3}+165x^{2}+6156x+2915x+166155\right)\left(x+5\right)$$

Combine 6156x and 2915x to get 9071x.

$$\left(x^{3}+165x^{2}+9071x+166155\right)\left(x+5\right)$$

Apply the distributive property by multiplying each term of x^{3}+165x^{2}+9071x+166155 by each term of x+5.

$$x^{4}+5x^{3}+165x^{3}+825x^{2}+9071x^{2}+45355x+166155x+830775$$

Combine 5x^{3} and 165x^{3} to get 170x^{3}.

$$x^{4}+170x^{3}+825x^{2}+9071x^{2}+45355x+166155x+830775$$

Combine 825x^{2} and 9071x^{2} to get 9896x^{2}.

$$x^{4}+170x^{3}+9896x^{2}+45355x+166155x+830775$$

Combine 45355x and 166155x to get 211510x.

$$x^{4}+170x^{3}+9896x^{2}+211510x+830775$$

Expand

$$x^{4}+170x^{3}+9896x^{2}+211510x+830775$$

Solution Steps

Apply the distributive property by multiplying each term of x+53 by each term of x+55.

$$\left(x^{2}+55x+53x+2915\right)\left(x+57\right)\left(x+5\right)$$

Combine 55x and 53x to get 108x.

$$\left(x^{2}+108x+2915\right)\left(x+57\right)\left(x+5\right)$$

Apply the distributive property by multiplying each term of x^{2}+108x+2915 by each term of x+57.

$$\left(x^{3}+57x^{2}+108x^{2}+6156x+2915x+166155\right)\left(x+5\right)$$

Combine 57x^{2} and 108x^{2} to get 165x^{2}.

$$\left(x^{3}+165x^{2}+6156x+2915x+166155\right)\left(x+5\right)$$

Combine 6156x and 2915x to get 9071x.

$$\left(x^{3}+165x^{2}+9071x+166155\right)\left(x+5\right)$$

Apply the distributive property by multiplying each term of x^{3}+165x^{2}+9071x+166155 by each term of x+5.

$$x^{4}+5x^{3}+165x^{3}+825x^{2}+9071x^{2}+45355x+166155x+830775$$

Combine 5x^{3} and 165x^{3} to get 170x^{3}.

$$x^{4}+170x^{3}+825x^{2}+9071x^{2}+45355x+166155x+830775$$

Combine 825x^{2} and 9071x^{2} to get 9896x^{2}.

$$x^{4}+170x^{3}+9896x^{2}+45355x+166155x+830775$$

Combine 45355x and 166155x to get 211510x.

$$x^{4}+170x^{3}+9896x^{2}+211510x+830775$$