(a - b)^2 Formula
The (a - b)2 formula says (a - b)2 = a2 - 2ab + b2. 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 = a2 - 2ab + b2. 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)
= a2 - ab - ba + b2
= a2 - 2ab + b2
Therefore, (a - b)2 formula is:
(a - b)2 = a2 - 2ab + b2
☛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 a2.
To prove that (a - b)2 = a2 - 2ab + b2, 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 b2. On rearranging the data we have (a − b)2 = a2 − ab − ab + b2. Hence this proves the algebraic identity (a − b)2 = a2 − 2ab + b2.
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 = a2 - 2ab + b2
(x - 2y)2 = (x)2 - 2(x)(2y) + (2y)2
= x2 - 4xy + 4y2
Answer: (x - 2y)2 = x2 - 4xy + 4y2.
Example 2: Factorize x2 - 6xy + 9y2 by using a minus b whole square formula.
Solution:
To factorize: x2 - 6xy + 9y2.
We can rearrange the given expression as:
x2 - 6xy + 9y2 = (x)2 - 2 (x) (3y) + (3y)2.
Using (a - b)2 formula:
a2 - 2ab + b2 = (a - b)2
Substitute a = x and b = 3y in this formula:
(x)2 - 2 (x) (3y) + (3y)2 = (x - 3y)2
Answer: x2 - 6xy + 9y2 = (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 = a2 - 2ab + b2
(7x - 4y)2 = (7x)2 - 2(7x)(4y) + (4y)2 = 49x2 - 56xy + 16y2.
Answer: (7x - 4y)2 = 49x2 - 56xy + 16y2.
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 = a2 - 2ab + b2.
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 = a2 - 2ab + b2
(20-5)2 = 202 - 2(20)(5) + 52
= 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 = a2 - 2ab + b2.
- 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 a2 + b2:
- Using (a + b)2 formula: a2 + b2 = (a + b)2 - 2ab
- Using (a - b)2 formula: a2 + b2 = (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 = a2 - 2ab + b2
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