Square of The Sum of Two Binomials
How to find the square of the sum of two binomials?
(a + b) (a + b) = a(a + b) + b(a + b)
= a2 + ab + ba + b2
= a2 + 2ab + b2
= a2 + b2+ 2ab
Therefore, (a + b)2 = a2 + b2 + 2ab
Square of the sum of two terms = square of 1st term + square of 2nd term + 2 × fist term × second term
This is called the binomial square.
It is stated as: the Square of the binomial (sum of two unlike term) is the square of the first term plus the square of the second term plus twice the product of two terms.
Worked-out examples on square of the sum of two binomials:
Solution:
We know, (a + b)2 = a2 + b2 + 2ab
Here, a = 2x and b = 3y
= (2x)2 + (3y)2 + 2 (2x) (3y)
= 4x2 + 9y2 + 12xy
Therefore, (2x + 3y)2 = 4x2 + 9y2 + 12xy.
2. Evaluate 1052 using the formula of (a + b)2.
Solution:
1052 = (100 + 5)2
We know, (a + b)2 = a2 + b2 + 2ab
Here, a = 100 and b = 5
(100 + 5)2
= (100)2 + (5)2 + 2 (100) (5)
= 10000 + 25 + 1000
= 11025
Therefore, 1052 = 11025.
3. Evaluate (10.1)2 using the identity.
Solution:
(10.1)2 = (10 + 0.1)2
We know, (a + b)2 = a2 + b2 + 2ab
Here, a = 10 and b = 0.1
(10 + 0.1)2
= (10)2 + (0.1)2 + 2 (10) (0.1)
= 100 + 0.01 + 2
= 102.01
Therefore, (10.1)2 = 102.01.
4. Use the formula of square of the sum of two terms to find the product of (1/5 x + 3/2 y) (1/5 x + 3/2 y).
Solution:
(1/5 x + 3/2 y) (1/5 x + 3/2 y) = (1/5 x + 3/2 y)2
We know that (a + b)2 = a2 + b2 + 2ab
Here, a = 1/5 x and b = 3/2 y
= (1/5 x)2 + (3/2 y)2 +
= 1/25 x2 + 9/4 y2 + 3/5 xy
Therefore, (1/5 x + 3/2 y) (1/5 x + 3/2 y) = 1/25 x2 + 9/4 y2 + 3/5 xy.
From the above solved problems we come to know square of a number means multiplying a number with itself, similarly, square of the sum of two binomial means multiplying the binomial with itself.
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