Solve (x-35)(x-15)(x-49)-35*35*(2x-102)-21*31*(x-49)

$$(x-35)(x-15)(x-49)-35 \times 35 \times (2x-102)-21 \times 31 \times (x-49)$$

Evaluate

$$x^{3}-99x^{2}-126x+131124$$

Solution Steps

Apply the distributive property by multiplying each term of x-35 by each term of x-15.

$$\left(x^{2}-15x-35x+525\right)\left(x-49\right)-35\times 35\left(2x-102\right)-21\times 31\left(x-49\right)$$

Combine -15x and -35x to get -50x.

$$\left(x^{2}-50x+525\right)\left(x-49\right)-35\times 35\left(2x-102\right)-21\times 31\left(x-49\right)$$

Apply the distributive property by multiplying each term of x^{2}-50x+525 by each term of x-49.

$$x^{3}-49x^{2}-50x^{2}+2450x+525x-25725-35\times 35\left(2x-102\right)-21\times 31\left(x-49\right)$$

Combine -49x^{2} and -50x^{2} to get -99x^{2}.

$$x^{3}-99x^{2}+2450x+525x-25725-35\times 35\left(2x-102\right)-21\times 31\left(x-49\right)$$

Combine 2450x and 525x to get 2975x.

$$x^{3}-99x^{2}+2975x-25725-35\times 35\left(2x-102\right)-21\times 31\left(x-49\right)$$

Multiply 35 and 35 to get 1225.

$$x^{3}-99x^{2}+2975x-25725-1225\left(2x-102\right)-21\times 31\left(x-49\right)$$

Use the distributive property to multiply -1225 by 2x-102.

$$x^{3}-99x^{2}+2975x-25725-2450x+124950-21\times 31\left(x-49\right)$$

Combine 2975x and -2450x to get 525x.

$$x^{3}-99x^{2}+525x-25725+124950-21\times 31\left(x-49\right)$$

Add -25725 and 124950 to get 99225.

$$x^{3}-99x^{2}+525x+99225-21\times 31\left(x-49\right)$$

Multiply 21 and 31 to get 651.

$$x^{3}-99x^{2}+525x+99225-651\left(x-49\right)$$

Use the distributive property to multiply -651 by x-49.

$$x^{3}-99x^{2}+525x+99225-651x+31899$$

Combine 525x and -651x to get -126x.

$$x^{3}-99x^{2}-126x+99225+31899$$

Add 99225 and 31899 to get 131124.

$$x^{3}-99x^{2}-126x+131124$$

Expand

$$x^{3}-99x^{2}-126x+131124$$

Solution Steps

Apply the distributive property by multiplying each term of x-35 by each term of x-15.

$$\left(x^{2}-15x-35x+525\right)\left(x-49\right)-35\times 35\left(2x-102\right)-21\times 31\left(x-49\right)$$

Combine -15x and -35x to get -50x.

$$\left(x^{2}-50x+525\right)\left(x-49\right)-35\times 35\left(2x-102\right)-21\times 31\left(x-49\right)$$

Apply the distributive property by multiplying each term of x^{2}-50x+525 by each term of x-49.

$$x^{3}-49x^{2}-50x^{2}+2450x+525x-25725-35\times 35\left(2x-102\right)-21\times 31\left(x-49\right)$$

Combine -49x^{2} and -50x^{2} to get -99x^{2}.

$$x^{3}-99x^{2}+2450x+525x-25725-35\times 35\left(2x-102\right)-21\times 31\left(x-49\right)$$

Combine 2450x and 525x to get 2975x.

$$x^{3}-99x^{2}+2975x-25725-35\times 35\left(2x-102\right)-21\times 31\left(x-49\right)$$

Multiply 35 and 35 to get 1225.

$$x^{3}-99x^{2}+2975x-25725-1225\left(2x-102\right)-21\times 31\left(x-49\right)$$

Use the distributive property to multiply -1225 by 2x-102.

$$x^{3}-99x^{2}+2975x-25725-2450x+124950-21\times 31\left(x-49\right)$$

Combine 2975x and -2450x to get 525x.

$$x^{3}-99x^{2}+525x-25725+124950-21\times 31\left(x-49\right)$$

Add -25725 and 124950 to get 99225.

$$x^{3}-99x^{2}+525x+99225-21\times 31\left(x-49\right)$$

Multiply 21 and 31 to get 651.

$$x^{3}-99x^{2}+525x+99225-651\left(x-49\right)$$

Use the distributive property to multiply -651 by x-49.

$$x^{3}-99x^{2}+525x+99225-651x+31899$$

Combine 525x and -651x to get -126x.

$$x^{3}-99x^{2}-126x+99225+31899$$

Add 99225 and 31899 to get 131124.

$$x^{3}-99x^{2}-126x+131124$$