(a + b)2 = a2 + 2ab + b2
Example 1: Find the value of (3x + 2y)2 using (a + b)2 formula.
Solution:
find the value of (3x + 2y)2
Let us assume that a = 3x and b = 2y.
We will substitute these values in (a + b)2 formula:
(a + b)2 = a2 + 2ab + b2
(3x+2y)2 =(3x)2 + 2(3x)(2y) +(2y)2
= 9x2+12xy+4y2
Example 2: Factorize x2 + 4xy + 4y2 using (a + b)2 formula.
Solution:
To
factorize : x2 + 4xy + 4y2
We can write the given expression as: (x)2 + 2 (x) (2y) + (2y)2.
Using (a + b)2 formula:
a2 + 2ab + b2 = (a + b)2
Substitute a = x and b = 2y in this formula:
(x)2 + 2 (x) (2y) + (2y)2. = (x + 2y)2
Example 3: Simplify the following using (a+b)2 formula.
Find the value of (7x + 4y)2
Solution:
a = 7x
and b = 4y
Using formula (a + b)2 = a2 + 2ab
+ b2
(7x)2 + 2(7x)(4y) + (4y)2
49x2 + 56xy + 16y2
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