What is (-3)^3+3(-3)^2+3(-3)+1 ?

The solution to (-3)^3+3(-3)^2+3(-3)+1 is -8

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(-3)^3+3(-3)^2+3(-3)+1

(- 3)^{3} + 3 (- 3)^{2} + 3 (- 3) + 1

- 8

Solution steps

(- 3)^{3} + 3 (- 3)^{2} + 3 (- 3) + 1

Follow the PEMDAS order of operations

Calculate exponents

(- 3)^{3} : - 27

(- 3)^{3}

Apply exponent rule:

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

n

is odd

(- 3)^{3} = - 3^{3} = - 27

= - 27

= - 27 + 3 (- 3)^{2} + 3 (- 3) + 1

Calculate exponents

(- 3)^{2} : 9

(- 3)^{2}

Apply exponent rule:

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

n

is even

(- 3)^{2} = 3^{2} = 9

= 9

= - 27 + 3 \cdot 9 + 3 (- 3) + 1

Multiply and divide (left to right)

3 \cdot 9 : 27

3 \cdot 9

3 \cdot 9 = 27

= 27

= - 27 + 27 + 3 (- 3) + 1

Multiply and divide (left to right)

3 (- 3) : - 9

3 (- 3)

Apply rule

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

3 (- 3) = - 3 \cdot 3 = - 9

= - 9

= - 27 + 27 - 9 + 1

Add and subtract (left to right)

- 27 + 27 - 9 + 1 : - 8

- 27 + 27 - 9 + 1

- 27 + 27 = 0

= 0 - 9 + 1

0 - 9 = - 9

= - 9 + 1

- 9 + 1 = - 8

= - 8

= - 8

5 8^{2} - 5 6^{2}

(- 3) + (- 2) (- 1) 2 (- 4)

6 - 2 - (- 7) - 3 + 6

2 + 2 - [1 - (- 1 + 23 - 19) + 17]

1 + 2 \times \frac{2}{5}