Solve 2(3-1)(15-2)^2+3(5-2*15)(15-1)^2-(15-2)(15-1)^2

$$2 ( 3 - 1 ) ( 15 - 2 ) ^ { 2 } + 3 ( 5 - 2 \times 15 ) ( 15 - 1 ) ^ { 2 } - ( 15 - 2 ) ( 15 - 1 ) ^ { 2 }$$

Evaluate

$$-16572$$

Solution Steps

Subtract 1 from 3 to get 2.

$$2\times 2\left(15-2\right)^{2}+3\left(5-2\times 15\right)\left(15-1\right)^{2}-\left(15-2\right)\left(15-1\right)^{2}$$

Multiply 2 and 2 to get 4.

$$4\left(15-2\right)^{2}+3\left(5-2\times 15\right)\left(15-1\right)^{2}-\left(15-2\right)\left(15-1\right)^{2}$$

Subtract 2 from 15 to get 13.

$$4\times 13^{2}+3\left(5-2\times 15\right)\left(15-1\right)^{2}-\left(15-2\right)\left(15-1\right)^{2}$$

Calculate 13 to the power of 2 and get 169.

$$4\times 169+3\left(5-2\times 15\right)\left(15-1\right)^{2}-\left(15-2\right)\left(15-1\right)^{2}$$

Multiply 4 and 169 to get 676.

$$676+3\left(5-2\times 15\right)\left(15-1\right)^{2}-\left(15-2\right)\left(15-1\right)^{2}$$

Multiply 2 and 15 to get 30.

$$676+3\left(5-30\right)\left(15-1\right)^{2}-\left(15-2\right)\left(15-1\right)^{2}$$

Subtract 30 from 5 to get -25.

$$676+3\left(-25\right)\left(15-1\right)^{2}-\left(15-2\right)\left(15-1\right)^{2}$$

Multiply 3 and -25 to get -75.

$$676-75\left(15-1\right)^{2}-\left(15-2\right)\left(15-1\right)^{2}$$

Subtract 1 from 15 to get 14.

$$676-75\times 14^{2}-\left(15-2\right)\left(15-1\right)^{2}$$

Calculate 14 to the power of 2 and get 196.

$$676-75\times 196-\left(15-2\right)\left(15-1\right)^{2}$$

Multiply -75 and 196 to get -14700.

$$676-14700-\left(15-2\right)\left(15-1\right)^{2}$$

Subtract 14700 from 676 to get -14024.

$$-14024-\left(15-2\right)\left(15-1\right)^{2}$$

Subtract 2 from 15 to get 13.

$$-14024-13\left(15-1\right)^{2}$$

Subtract 1 from 15 to get 14.

$$-14024-13\times 14^{2}$$

Calculate 14 to the power of 2 and get 196.

$$-14024-13\times 196$$

Multiply 13 and 196 to get 2548.

$$-14024-2548$$

Subtract 2548 from -14024 to get -16572.

$$-16572$$

Factor

$$-16572$$