Examples on a2 – b2 Formula
Example 1: Simplify x2 – 16
Solution:
= x2 – 16
= x2 – 42
We know that, a2 – b2 = (a+b) (a–b)
Given,
- a = x
- b = 4
= (x + 4)(x – 4)
Example 2: Simplify 9y2 – 144
Solution:
= 9y2 – 144
= (3y)2 – (12)2
We know that, a2 – b2 = (a+b)(a–b)
Given,
- a = 3y
- b = 12
= (3y + 12)(3y – 12)
Example 3: Simplify (3x + 2)2 – (3x – 2)2
Solution:
We know that,
a2 – b2 = (a+b)(a–b)
Given,
- a = 3x + 2
- b = 3x – 2
(3x + 2)2 – (3x – 2)2
= (3x + 2 + 3x – 2)(3x + 2 – (3x – 2))
= 6x(3x + 2 – 3x + 2)
= 6x(4)
= 24x
Example 4: Simplify y2 – 100
Solution:
= y2 – 100
= y2 – (10)2
We know that,
a2 – b2 = (a+b)(a–b)
Given,
- a = y
- b = 10
= (y + 10)(y – 10)
Example 5: Evaluate (x + 6) (x – 6)
Solution:
We know that,
(a+b) (a–b) = a2 – b2
Given,
- a = x
- b = 6
(x + 6) (x – 6)
= x2 – 62
= x2 – 36
Example 6: Evaluate (y + 13)(y – 13)
Solution:
We know that,
(a+b) (a–b) = a2 – b2
Given,
- a = y
- b = 13
(y + 13).(y – 13)
= y2 – (13)2
= y2 – 169
Example 7: Evaluate (x + y + z).(x + y – z)
Solution:
We know that,
(a+b) (a–b) = a2 – b2
Given,
- a = x + y
- b = z
(x + y + z) (x + y – z)
= (x + y)2 – z2
= x2 + y2 + 2xy – z2
a2 – b2 Formula
a2 – b2 formula in Algebra is the basic formula in mathematics used to solve various algebraic problems. a2 – b2 formula is also called the difference of square formula, as this formula helps us to find the difference between two squares without actually calculating the squares. The image added below shows the formula of a2 – b2
In this article, we will learn the a2 – b2 formula, a2 – b2 identity, examples, and others in detail.
Table of Content
- What is a2 – b2 Formula?
- Difference of Squares Formula
- a2 – b2 Square Formula Proof
- (a + b)2 and (a – b)2 Formula
- a2 – b2 Identity