# The Quarterly Journal Of Pure And Applied Mathematics

The (a -b)^3formula is used to find the cubeof a binomial. This formula is also used khổng lồ factorize some special types of trinomials. This formula is one of the algebraic identities. The (a-b)^3 formula is the formula for the cubeof the differenceof two terms. This formula is used to calculate the cube of the difference of two terms very easily và quickly without doing complicated calculations. Let us learn more about(a-b)^3 formula along with solved examples.

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## What Is the (a -b)^3 Formula?

The (a-b)^3 formula is used to lớn calculate thecubeof a binomial. The formula is also known as the cube of the difference between two terms. To find the formula of (a -b)3, we will just multiply (a -b)(a -b) (a -b).

(a -b)3=(a -b)(a - b)(a -b)

= (a2-2ab + b2)(a -b)

= a3- a2b -2a2b +2ab2+ ab2-b3

= a3-3a2b + 3ab2-b3

= a3-3ab(a-b) -b3

Therefore,(a -b)3formula is:

(a -b)3= a3-3a2b + 3ab2-b3

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## Examples on(a -b)^3Formula

**Example 1:**Solve the following expression using (a -b)3formula:(2x -3y)3

**Solution:**

To find: (2x - 3y)3Using (a -b)3Formula,(a -b)3=a3-3a2b + 3ab2-b3= (2x)3-3× (2x)2× 3y + 3× (2x)× (3y)2-(3y)3= 8x3-36x2y + 54xy2-27y3

**Answer: (2x -3y)3 = 8x3-36x2y + 54xy2-27y3**

**Example 2:**Find the value of x3-y3if x -y = 5and xy = 2 using (a -b)3formula.

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**Solution:**

To find: x3-y3Given:x -y = 5xy = 2Using (a -b)3Formula,(a -b)3=a3-3a2b + 3ab2-b3Here, a = x; b = yTherefore,(x -y)3= x3-3×x2× y+ 3 × x× y2-y3 (x -y)3= x3-3x2y + 3xy2-y353=x3-3xy(x -y) -y3125= x3-3× 2× 5- y3x3-y3= 95

**Answer: x3-y3= 95**

**Example 3:**Solve the following expression using (a -b)3formula:

(5x - 2y)3

**Solution:**

To find: (5x - 2y)3Using (a -b)3Formula,(a -b)3=a3-3a2b + 3ab2-b3= (5x)3-3× (5x)2× 2y + 3× (5x)× (2y)2-(2y)3= 125x3-150x2y + 60xy2-8y3

**Answer: (5x -2y)3 = 125x3-150x2y + 60xy2-8y3**

## FAQs on (a -b)^3Formula

### What Is the Expansion of (a -b)3Formula?

(a -b)3formula is read as a minus b whole cube. Its expansion is expressed as(a -b)3=a3-3a2b + 3ab2-b3

### What Is the(a -b)3Formula in Algebra?

The (a -b)3formula is also known as one of the importantalgebraic identities. It is read as aminus b whole cube. Its (a -b)3formula is expressed as(a -b)3=a3-3a2b + 3ab2-b3How lớn Simplify Numbers Usingthe(a -b)3Formula?

Let us understand the use of the (a -b)3formula with the help of the following example.**Example:**Find the value of (20- 5)3using the (a -b)3formula.To find:(20- 5)3Let us assume that a = 20 & b = 5.We will substitute these in the formula of(a- b)3.(a -b)3=a3-3a2b + 3ab2-b3(20-5)3= 203 - 3(20)2(5) + 3(20)(5)2- 53= 8000 - 6000 + 1500 - 125= 3375**Answer:**(20-5)3= 3375.

### How lớn Use the(a -b)3Formula?

The following steps are followed while using(a -b)3formula.

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