# a square minus b square formula explained

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. 