Square of The Difference of Two Binomials
How to find the square of the difference 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 difference 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 difference of two binomials (two unlike terms) is the square of the first term plus the second term minus twice the product of the first and the second term.
Worked-out examples on square of the difference of two binomials:
Solution:
Square of 1st term + square of 2nd term - 2 × fist term × second term
Here, a = 4x and y = 7y
= (4x)2 + (7y)2 - 2 (4x) (7y)
= 16x2 + 49y2 - 56xy
Therefore, (4x + 7y)2 = 16x2 + 49y2 - 56xy.
2. Expand (3m - 5/6 n)2 using the formula of (a - b)2.
Solution:
We know (a - b)2 = a2 + b2 - 2ab
Here, a = 3m and b = 5/6 n
= (3m)2 + (5/6 n)2 - 2 (3m) (5/6 n)
= 9 m2 + 25/36 n2 -
= 9 m2 + 25/36 n2 - 5 mn
Therefore, (3m - 5/6 n)2 = 9 m2 + 25/36 n2 - 5 mn.
3. Evaluate (999)2 using the identity.
Solution:
(999)2 = (1000 – 1)2
We know, (a – b)2 = a2 + b2 – 2ab
Here, a = 1000 and b = 1
(1000 – 1)2
= (1000)2 + (1)2 – 2 (1000) (1)
= 1000000 + 1 – 2000
= 998001
Therefore, (999)2 = 998001
4. Use the formula of square of the difference of two terms to find the product of (0.1 m – 0.2 n) (0.1 m – 0.2 n).
Solution:
(0.1 m – 0.2 n) (0.1 m – 0.2 n) = (0.1 m – 0.2 n)2
We know (a – b)2 = a2 + b2 – 2ab
Here, a = 0.1 m and b = 0.2 n
= (0.1 m)2 + (0.2 n) 2 - 2 (0.1 m) (0.2 n)
= 0.01 m2 + 0.04 n2 - 0.04 mn
Therefore, (0.1 m – 0.2 n) (0.1 m – 0.2 n) = 0.01 m2 + 0.04 n2 - 0.04 mn
From the above solved problems we come to know square of a number means multiplying a number with itself, similarly, square of the difference of two binomial means multiplying the binomial by itself.
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