Topic Content:
- Difference of Two Squares
(x + a) (x – a) = x(x – a ) + a (x – a )
= x2 – ax + ax – a2
= x2 – a2
The above result is called the difference of two squares.
We can state the above relation as follows:
The difference of two squares is equal to the product of their sum and their difference.
Worked Example 7.2.1:
Factorize the following expression completely:
i. p2 – q2
ii. (x2 – a2)
iii. 22 – t2
iv. 16s2 – 4t2
v. 121 – 9y2
Solution
i. p2 – q2 = (p – q) (p + q)
This is true because:
⇒ p (p + q) – q (p + q)
⇒ p2 + pq – pq – q2
= p2 – q2
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