# FORMULA FOR A SQUARED MINUS B SQUARE

On this webpage formula for a squared minus b square, that is (a² - b²)  we are going to see some example problems based on this formula.

## What is Algebraic identity?

An identity is an equality that remains true regardless of the values of any variables that appear within it.

Now let us see the

## formula for a squared minus b square

Question 1 :

Expand (5x)² - 3 ²

Solution:

Here the question is in the form of (a²- b²) . Instead of a we have "5x" and instead of b we have "3" . So we need to apply the formula (a + b) (a - b) and we need to apply those values instead of a and b

(5x)² - 3² = (5x + 3) (5x - 3)

Question 2 :

Expand x² - 1 ²

Solution:

Here the question is in the form of (a²-b²) ². Instead of a we have "x" and instead of b we have "1" . So we need to apply the formula for square .That is (a + b)(a - b) and we need to apply those values instead of a and b

x² - 1² = (x + 1) (x-1)

Question 3:

Expand 16 x² - 9

Solution

We can split the first term 16 as 4x4 and 9 as 3x3.Instead of this we can write

= 4 ²x² - 3²

= (4x)² - 3 ²

= (4x + 3) (4x - 3)

Now we are going to see some different questions using this topic.

Question 4:

If x/y = 6/5,find the value of (x² + y²)/(x² - y²)

Solution

= (x² + y²)/(x² - y²)

Now,we are going to divide the whole thing by y².

= [ (x²/y²) + 1 ]/[ (x²/y²) - 1 ]

x/y = 6/5

taking squares on both sides,

(x/y)² = (6/5)²

x²/y² = 36/25

= [ (36/25) + 1 ]/[ (36/25) - 1 ]

= [ (36 + 25)/25 ]/[ (36 - 25)/25 ]

= [ 61/25 ]/[ 11/25 ]

= 61/11

Question 5:

Find the value of (75983 x 75983 - 45983 x 45983)/30000

Solution

= (75983 x 75983 - 45983 x 45983)/30000

= [ (75983)² - (45983)² ]/[ 75983 - 45983 ]

= [ (75983 + 45983) (75983 - 45983) ]/[ 75983 - 45983 ]

=  (75983 + 45983)

=  (75983 + 45983)

=  121966

(a - b)² = a² - 2 ab + b²

a² - b² = (a + b) (a - b)

(x+a)(x+b)=x²+(a+b)x+ab

(a+b)³=a³+3a²b+3ab²+b³

(a-b)³=a³-3a²b+3ab²-b³

(a³+b³)= (a+b)(a²-ab+b²)

(a³-b³)=(a-b)(a²+ab+ b²)

(a+b+c)²= a²+b²+c²+2ab+2bc+2ca