Learn and know the **formula for a square minus b square**. In algebra, this is the one of important and very useful formula. We also say **a square minus b square **formula as an identity.

I said **a square minus b square formula **is a identity. Do you know why it is called as an identity? In the formula, for any values of a and b, we get L.H.S is equals to R.H.S. so like this formulas we call it as an identity. The other identities are a plus b whole cube, a minus b whole cube, a plus b whole square, a minus b whole square and so on.

**The formula for** **a square minus b square is given below:**

Mathematically, we can write **a square minus b square **as** { a }^{ 2 } – { b }^{ 2 } . **So, therefore ** { a }^{ 2 } – { b }^{ 2 } **** = **(a + b)×(a – b)**, where a and b are variables.**

The above formula is written as a square minus b square is equal to a plus b multiplied with a minus b.

NOTE:

If “a” and “b” are any two consecutive numbers then **a square minus b square = a plus b**. To know and understand about this point refer example number 3.

Examples:

♦ Solve: ** { 9 }^{ 2 } ** – ** { 4 }^{ 2 } **

Solution:

We know that a square minus b square is equal to a plus b multiplied with a minus b i.e. ** { a }^{ 2 } – { b }^{ 2 } ** equals to (a + b)×(a – b)

So, ** { 9 }^{ 2 } ** – ** { 4 }^{ 2 } ** = (9+4) **×** (9-4) = 13 **×** 5 = 65.

♦ Solve: ** { 52 }^{ 2 } ** – ** { 45 }^{ 2 } **

Solution:

According to **a square minus b square formula,**

** { 52 }^{ 2 } ** – ** { 45 }^{ 2 } ** = (52+45) **×** (52-45) = 97 **×** 7 = 679

♦ Solve: ** { 28 }^{ 2 } ** – ** { 27 }^{ 2 } **

Solution:

** { 28 }^{ 2 } ** – ** { 27 }^{ 2 } ** = (28+27) **×** (28-27) = 55 **×** 1 = 55

Hope you have learnt a square minus b square formula and also examples.

## Leave a Reply