Perfect Square Formula
The perfect square formula used to find the square of the addition or subtraction of two polynomials, (a ± b)2 and is known as the perfect square formula.
Let's learn more about the sum of the perfect square formula with a few solved examples.
What is the Perfect Square Formula?
The perfect square formula is:
(a ± b)2 = (a2 ± 2ab + b2)
or
Solved Examples Using Perfect Square Formula
Example1: Find the square of 6x + 4y.
Solution:
To find: Square of 6x + 4y,
Using the perfect square formula.
(a + b)2 = (a2 + 2ab + b2)
Put the values,
(6x + 4y)2 = ((6x)2 + 2 × 6x × 4y + (4y)2)
(6x + 4y)2= (36x2 + 48x + 16y2)
Answer: The the square of 6x + 4y is (36x2 + 48x + 16y2).
Example 2:
Find if x2 + 25 - 10x is perfect square or not.
Solution:
To find: x2 + 25 - 10x is perfect square or not.
Rearranging the terms:
x2 + 25 - 10x = x2 + 5 × 5 - 2 × 5 × x = x2 - 2 × 5 × x + 5 × 5
Using the perfect square formula.
(a - b)2 = (a2 - 2ab + b2)
Comparing the values,
x2 - 2 × 5 × x + 5 × 5 = (x - 5)2
Answer: x2 + 25 - 10x is perfect square.
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