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