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.

a square minus b square formula

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.

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