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)
= a
^{2} + ab + ba + b
^{2}
= a
^{2} + 2ab + b
^{2}
= a
^{2} + b
^{2}+ 2ab
Therefore, (a + b)
^{2} = a
^{2} + b
^{2} + 2ab
Square of the sum of two terms = square of 1
^{st} term + square of 2
^{nd} 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:
1. Expand (2x + 3y)
^{2}, using suitable identity.
Solution:
We know, (a + b)
^{2} = a
^{2} + b
^{2} + 2ab
Here, a = 2x and b = 3y
= (2x)
^{2} + (3y)
^{2} + 2 (2x) (3y)
= 4x
^{2} + 9y
^{2} + 12xy
Therefore, (2x + 3y)
^{2} = 4x
^{2} + 9y
^{2} + 12xy.
2. Evaluate 105
^{2} using the formula of (a + b)
^{2}.
Solution:
105
^{2} = (100 + 5)
^{2}
We know, (a + b)
^{2} = a
^{2} + b
^{2} + 2ab
Here, a = 100 and b = 5
(100 + 5)
^{2}
= (100)
^{2} + (5)
^{2} + 2 (100) (5)
= 10000 + 25 + 1000
= 11025
Therefore, 105
^{2} = 11025.
3. Evaluate (10.1)
^{2} using the identity.
Solution:
(10.1)
^{2} = (10 + 0.1)
^{2}
We know, (a + b)
^{2} = a
^{2} + b
^{2} + 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} = a
^{2} + b
^{2} + 2ab
Here, a = 1/5 x and b = 3/2 y
= (1/5 x)
^{2} + (3/2 y)
^{2} +
2 (1/5 x) (3/
2 y)
= 1/25 x
^{2} + 9/4 y
^{2} + 3/5 xy
Therefore, (1/5 x + 3/2 y) (1/5 x + 3/2 y) = 1/25 x
^{2} + 9/4 y
^{2} + 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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7th Grade Math Problems
8th Grade Math Practice
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