What is the formula for a³ + b³?
Solution
The cube of a number means multiplying the number by itself three times.
For example:
a³ = a × a × a
The algebraic identity for the sum of cubes of two numbers is:
a³ + b³ = (a + b)(a² − ab + b²)
Explanation
- a and b are any two numbers or algebraic terms.
- The expression a³ + b³ is called the sum of cubes.
- This identity helps us factorise the expression easily.
Understanding the Formula
The formula has two parts:
- First factor: (a + b)
- Second factor: (a² − ab + b²)
When these two factors are multiplied together, we get:
a³ + b³
Example
Factorise x³ + 2³.
Using the formula:
a³ + b³ = (a + b)(a² − ab + b²)
Here, a = x and b = 2.
x³ + 2³ = (x + 2)(x² − 2x + 4)
Final Note
- Always write the formula first.
- Then substitute the values of a and b.
- Keep the steps neat and clear to get full marks.
a³ + b³ = (a + b)(a² − ab + b²)