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

(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