In this topic square formula, we are going to discuss about two formulas which are being used to expand the terms like in the form (a + b) ². This particular formula (a + b) ² plays a vital role in math from 8 th grade, 9 th grade, 10 th grade to higher studies.
A students who studies math in his school days can never miss this formula. Particularly in the topic Algebra, we can solve many problems by using this formula. 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.
Question 1 :
Expand (5x + 3) ²
Solution:
Here the question is in the form of (a+b)². Instead of a we have "5x" and instead of b we have "3" . So we need to apply the formula a² + 2ab + b ² and we need to apply those values instead of a and b
(5x + 3)² = (5x)² + 2 (5x) (3) + (3)²
= 25x² + 30 x + 9
= 25x² + 30 x + 9 square formula
Question 2 :
Expand (x + 2) 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 "2" . So we need to apply the formula a² + 2ab + b ² and we need to apply those values instead of a and b
(x + 2)² = (x)² + 2 (x) (2) + (2)²
= x² + 4 x + 4
Question 3 :
If a - b = 3 and a² + b² = 29,find the value of ab.
Solution:
(a - b)² = a² + b² - 2 a b
3² = 29 - 2ab
9 = 29 - 2 ab
2 a b = 29 - 9
2 a b = 20
ab = 20/2
ab = 10
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
= 4 + (1/2)
= 9/2
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