In this post we will learn to find the cube of negative numbers with example.

If you want the revise the basics of** cube of any number**, click the red link.

## Cube of negative number

The cube of negative number is found by **multiplying the number by itself thrice**.

When we multiply the negative number thrice by itself we get the **negative number**.

Hence, the cube of negative number is also a negative number.

The **general form of cube of negative number** is given as;

\mathtt{( -m)^{3} \Longrightarrow ( -m) \times ( -m) \times ( -m) \ }\\\ \\ \mathtt{( -m)^{3} \Longrightarrow \ -m^{3}}

### Rules of negative sign multiplication

To understand the cube of negative number, just remember the below rule.

(a) **Multiplication of two negative sign results in positive sign.**

It’s like two negatives becoming positive.

(b) When** we multiply three negative signs, the final result is also negative**.

From the below image you can see that **cube of negative number works in three steps**;

(i) Two negative numbers multiply to generate positive number.

(ii) The positive number will them multiply the negative number to generate negative number.

**For example;**

Find the cube of -5

Multiply -5 by itself three times

\mathtt{\Longrightarrow \ ( -5)^{3}}\\\ \\ \mathtt{\Longrightarrow \ ( -5) \times ( -5) \times ( -5)}\\\ \\ \mathtt{\Longrightarrow \ -125}

Hence, on calculation we got the negative number.

**Example 02**

Find the cube of -11

**Solution**

Multiply -11 by itself three times.

\mathtt{\Longrightarrow \ ( -11)^{3}}\\\ \\ \mathtt{\Longrightarrow \ ( -11) \times ( -11) \times ( -11)}\\\ \\ \mathtt{\Longrightarrow \ -133}

**Example 03**

Find the cube of -12

**Solution**

Multiply -12 thrice.

\mathtt{\Longrightarrow \ ( -12)^{3}}\\\ \\ \mathtt{\Longrightarrow \ ( -12) \times ( -12) \times ( -12)}\\\ \\ \mathtt{\Longrightarrow \ 144\times ( -12)}\\\ \\ \mathtt{\Longrightarrow \ -1728}

Hence, cube of -12 is -1728.

**Example 04**

Find the cube of -25

**Solution**

Multiply -25 thrice.

\mathtt{\Longrightarrow \ ( -25)^{3}}\\\ \\ \mathtt{\Longrightarrow \ ( -25) \times ( -25) \times ( -25)}\\\ \\ \mathtt{\Longrightarrow \ 625\ \times ( -25)}\\\ \\ \mathtt{\Longrightarrow \ -15625}

Hence, **cube of -25 is -15625**.