Solve 2(3-1)(1.5-2)^2+3(5-2*1.5)(1.5-1)^2-(1.5-2)(1.5-1)^2

$$2 ( 3 - 1 ) ( 1.5 - 2 ) ^ { 2 } + 3 ( 5 - 2 \times 1.5 ) ( 1.5 - 1 ) ^ { 2 } - ( 1.5 - 2 ) ( 1.5 - 1 ) ^ { 2 }$$

Evaluate

$$2.625$$

Solution Steps

Subtract 1 from 3 to get 2.

$$2\times 2\left(1.5-2\right)^{2}+3\left(5-2\times 1.5\right)\left(1.5-1\right)^{2}-\left(1.5-2\right)\left(1.5-1\right)^{2}$$

Multiply 2 and 2 to get 4.

$$4\left(1.5-2\right)^{2}+3\left(5-2\times 1.5\right)\left(1.5-1\right)^{2}-\left(1.5-2\right)\left(1.5-1\right)^{2}$$

Subtract 2 from 1.5 to get -0.5.

$$4\left(-0.5\right)^{2}+3\left(5-2\times 1.5\right)\left(1.5-1\right)^{2}-\left(1.5-2\right)\left(1.5-1\right)^{2}$$

Calculate -0.5 to the power of 2 and get 0.25.

$$4\times 0.25+3\left(5-2\times 1.5\right)\left(1.5-1\right)^{2}-\left(1.5-2\right)\left(1.5-1\right)^{2}$$

Multiply 4 and 0.25 to get 1.

$$1+3\left(5-2\times 1.5\right)\left(1.5-1\right)^{2}-\left(1.5-2\right)\left(1.5-1\right)^{2}$$

Multiply 2 and 1.5 to get 3.

$$1+3\left(5-3\right)\left(1.5-1\right)^{2}-\left(1.5-2\right)\left(1.5-1\right)^{2}$$

Subtract 3 from 5 to get 2.

$$1+3\times 2\left(1.5-1\right)^{2}-\left(1.5-2\right)\left(1.5-1\right)^{2}$$

Multiply 3 and 2 to get 6.

$$1+6\left(1.5-1\right)^{2}-\left(1.5-2\right)\left(1.5-1\right)^{2}$$

Subtract 1 from 1.5 to get 0.5.

$$1+6\times 0.5^{2}-\left(1.5-2\right)\left(1.5-1\right)^{2}$$

Calculate 0.5 to the power of 2 and get 0.25.

$$1+6\times 0.25-\left(1.5-2\right)\left(1.5-1\right)^{2}$$

Multiply 6 and 0.25 to get 1.5.

$$1+1.5-\left(1.5-2\right)\left(1.5-1\right)^{2}$$

Add 1 and 1.5 to get 2.5.

$$2.5-\left(1.5-2\right)\left(1.5-1\right)^{2}$$

Subtract 2 from 1.5 to get -0.5.

$$2.5-\left(-0.5\left(1.5-1\right)^{2}\right)$$

Subtract 1 from 1.5 to get 0.5.

$$2.5-\left(-0.5\times 0.5^{2}\right)$$

Calculate 0.5 to the power of 2 and get 0.25.

$$2.5-\left(-0.5\times 0.25\right)$$

Multiply -0.5 and 0.25 to get -0.125.

$$2.5-\left(-0.125\right)$$

The opposite of -0.125 is 0.125.

$$2.5+0.125$$

Add 2.5 and 0.125 to get 2.625.

$$2.625$$

Factor

$$\frac{3 \cdot 7}{2 ^ {3}} = 2\frac{5}{8} = 2.625$$