In this topic square formulas we are going to discuss about two formulas which are being used to expand the terms like in the form (a - b) ². We are going to see some of the example problem.
After getting clear of using this you can try the worksheet also.We have given 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.
Expand (2x - 3) ²
Solution:
Here the question is in the form of (a-b) ². Instead of a we have "2x" and instead of b we have "3" . Now we need to apply the formula a² - 2ab + b ² and we need to apply those values instead of a and b
(2x - 3)² = (2x)² - 2 (2x) (3) + (3)²
= 4x² - 12 x + 9
Question 2 :
Expand (x - 5) ²
Solution:
Here the question is in the form of (a-b) ². Instead of a we have "x" and instead of b we have "5" . Now we need to apply the formula a² - 2ab + b ² and we need to apply those values instead of a and b
(x - 5)² = (x)² - 2 (x) (5) + (5)²
= x² - 10 x + 25
Question 3 :
Expand (3x - 7) ²
Solution:
Here the question is in the form of (a-b) ². Instead of a we have "3x" and instead of b we have "7" . Now we need to apply the formula a² - 2ab + b ² and we need to apply those values instead of a and b
(3x - 7)² = ( 3 x )² - 2 ( 3 x ) ( 7 ) + ( 7 )²
= 3²x² - 6 x ( 7 ) + 49
= 9 x² - 42 x + 49
Question 4 :
[√2 - (1/√
2)]² is equal to
Solution:
(a - b)² = a² + b² - 2 a b
a = √2 b = 1/√2
[√2 - (1/√ 2)]² = ( √2 )² + (1/√2)² - 2 √2 (1/√2)
= 2 + (1/2) - 2
= (1/2)
We are using this formulas in many of the problems in algebra.We can easily memo rise this by reading this formula by comparing.
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