# (a - b)^2 Formula

The **(a - b) ^{2} formula** says (a - b)

^{2}= a

^{2}- 2ab + b

^{2}. It is used to find the square of a binomial. This a minus b whole square formula is one of the commonly used algebraic identities. This formula is also known as the formula for the square of the difference between two terms.

The (a - b)^{2} formula is used to factorize some special types of trinomials. Let us learn more about a minus b Whole Square along with solved examples in the following section.

## What is (a - b)^2 Formula?

The (a - b)^{2} formula is also widely known as the square of the difference between the two terms. It says (a - b)^{2} = a^{2} - 2ab + b^{2}. This formula is sometimes used to factorize the binomial. To find the formula of (a - b)^{2}, we will just multiply (a - b) (a - b).

(a - b)^{2 }= (a - b)(a - b)

= a^{2} - ab - ba + b^{2}

= a^{2} - 2ab + b^{2}

Therefore, (a - b)^{2} formula is:

(a - b)^{2} = a^{2} - 2ab + b^{2}

**☛Also Check: **(a + b)^2 Formula

### Proof of A minus B Whole Square Formula

Let us consider (a - b)^{2} as the area of a square with length (a - b). In the above figure, the biggest square is shown with area a^{2}.

To prove that (a - b)^{2} = a^{2} - 2ab + b^{2}, consider reducing the length of all sides by factor b, and it forms a new square of side length a - b. In the figure above, (a - b)^{2} is shown by the blue area. Now subtract the vertical and horizontal strips that have the area a × b. Removing a × b twice will also remove the overlapping square at the bottom right corner twice hence add b^{2}. On rearranging the data we have (a − b)^{2} = a^{2} − ab − ab + b^{2}. Hence this proves the algebraic identity (a − b)^{2} = a^{2} − 2ab + b^{2}.

## Examples on (a **- **b)^2 Formula

**Example 1:** Find the value of (x - 2y)^{2 }by using the (a - b)^{2} formula.

**Solution: **

To find: The value of (x - 2y)^{2}.

Let us assume that a = x and b = 2y.

We will substitute these values in (a - b)^{2} formula:

(a - b)^{2} = a^{2} - 2ab + b^{2}

(x - 2y)^{2 }= (x)^{2} - 2(x)(2y) + (2y)^{2 }

= x^{2 }- 4xy + 4y^{2}

**Answer: **(x - 2y)^{2} = x^{2} - 4xy + 4y^{2}.

**Example 2:** Factorize x^{2} - 6xy + 9y^{2 }by using a minus b whole square formula.

**Solution: **

To factorize: x^{2} - 6xy + 9y^{2}.

We can rearrange the given expression as:

x^{2} - 6xy + 9y^{2} = (x)^{2} - 2 (x) (3y) + (3y)^{2}.

Using (a - b)^{2} formula:

a^{2} - 2ab + b^{2} = (a - b)^{2}

Substitute a = x and b = 3y in this formula:

(x)^{2} - 2 (x) (3y) + (3y)^{2} = (x - 3y)^{2}

**Answer: **x^{2} - 6xy + 9y^{2} = (x - 3y)^{2}.

**Example 3:** Simplify the following using the (a - b)^{2} formula: (7x - 4y)^{2}.

**Solution:**

a = 7x and b = 4y

Using formula (a - b)^{2} = a^{2} - 2ab + b^{2}

(7x - 4y)^{2} = (7x)^{2} - 2(7x)(4y) + (4y)^{2} = 49x^{2} - 56xy + 16y^{2}.

**Answer:** (7x - 4y)^{2} = 49x^{2} - 56xy + 16y^{2}.

## FAQs on A minus B Whole Square Formula

### What is the Expansion of (a - b)^{2} Formula?

**(a - b) ^{2} formula** is read as a minus b whole square. Its expansion is expressed as (a - b)

^{2}= a

^{2}- 2ab + b

^{2}.

### How to Simplify Numbers Using the A - B Whole Square Formula?

Let us understand the use of the (a - b)^{2} formula with the help of the following example.

**Example:** Find the value of (20 - 5)^{2} using the (a - b)^{2} formula.

To find: (20 - 5)^{2}

Let us assume that a = 20 and b = 5.

We will substitute these in the formula of (a - b)^{2}.

(a - b)^{2} = a^{2} - 2ab + b^{2}

(20-5)^{2} = 20^{2} - 2(20)(5) + 5^{2}

= 400 - 200 + 25

= 225

**Answer:** (20 - 5)^{2} = 225.

### How to Use the (a - b)^{2} Formula Give Steps?

The following steps are followed while using the (a - b)^{2} formula.

- Write down the formula of (a - b)
^{2}: (a - b)^{2}= a^{2}- 2ab + b^{2}. - Substitute the values of a and b in the above formula and simplify.

### What is the Formula for a Square Plus b Square?

We have two formulas for a^{2} + b^{2}:

- Using (a + b)
^{2}formula: a^{2}+ b^{2}= (a + b)^{2}- 2ab - Using (a - b)
^{2}formula: a^{2}+ b^{2}= (a - b)^{2}+ 2ab

### What is the a - b Whole Square Formula in Algebra?

The (a - b)^{2} formula is one of the important algebraic identities. It is read as a minus b whole square. a - b whole square formula is expressed as (a - b)^{2} = a^{2} - 2ab + b^{2}

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