# Cube of negative number

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.