Formula For Square





In this topic formula for square we are going to discuss about the formula which are being used to expand the terms like in the form (a² - b²). We are going to see some of the example problem.After getting clear of using this you can try the worksheet also.

We are giving this worksheet for the purpose of making practice.If you practice this worksheets it will become easy to face problems in the topic algebra.We will use these formulas in most of the problem.

Examples of formula for 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


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