(-2)^3 - (-2 + 1)^3 — step-by-step solution

Let's calculate:

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

ⓘ Powers are computed before multiplications, additions and subtractions. An integer power is a repeated product:

{(-2)}^{3}

(-2) \times (-2) \times (-2)

-8

■Parentheses are computed first:

- 2 + 1

-1

- 8 - {(-1)}^{3}

ⓘ An integer power is a repeated product:

- {(-1)}^{3}

- ((-1) \times (-1) \times (-1))

- (-1)

- 8 - (-1)

ⓘ Subtracting a negative number is adding it, two minus signs make a plus:

- (-1)

1

- 8 + 1

ⓘ Start from

-8

and move forward

1

on the number line, getting closer to zero:

- 8 + 1

-7

▶Result:

-7