What is (-2)^3+3(-2)^2+2(-2)-5 ?

The solution to (-2)^3+3(-2)^2+2(-2)-5 is -5

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(-2)^3+3(-2)^2+2(-2)-5

(- 2)^{3} + 3 (- 2)^{2} + 2 (- 2) - 5

- 5

Solution steps

(- 2)^{3} + 3 (- 2)^{2} + 2 (- 2) - 5

Follow the PEMDAS order of operations

Calculate exponents

(- 2)^{3} : - 8

(- 2)^{3}

Apply exponent rule:

(- a)^{n} = - a^{n},

n

is odd

(- 2)^{3} = - 2^{3} = - 8

= - 8

= - 8 + 3 (- 2)^{2} + 2 (- 2) - 5

Calculate exponents

(- 2)^{2} : 4

(- 2)^{2}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

(- 2)^{2} = 2^{2} = 4

= 4

= - 8 + 3 \cdot 4 + 2 (- 2) - 5

Multiply and divide (left to right)

3 \cdot 4 : 12

3 \cdot 4

3 \cdot 4 = 12

= 12

= - 8 + 12 + 2 (- 2) - 5

Multiply and divide (left to right)

2 (- 2) : - 4

2 (- 2)

Apply rule

a \cdot (- b) = - a \cdot b

2 (- 2) = - 2 \cdot 2 = - 4

= - 4

= - 8 + 12 - 4 - 5

Add and subtract (left to right)

- 8 + 12 - 4 - 5 : - 5

- 8 + 12 - 4 - 5

- 8 + 12 = 4

= 4 - 4 - 5

4 - 4 = 0

= 0 - 5

0 - 5 = - 5

= - 5

= - 5

(4 - 3)^{3}

\frac{1}{2} - (\frac{2}{3} + \frac{1}{2})

1 7^{2} + 1 2^{2}

5 + 6 \times 4 - 7 \div 3

- 2 \cdot (5 \cdot 3 - 5) \div 2