Strange products » Difference of squares
The rule:
(a + b)(a – b) = a2 – b2
Why is this true?
The normal rule is:
(a + b)(c – d) = ac – ad + bc – bd
When we choose a and b also for c and d, we get:
(a + b)(a – b) = a2 – ab + ab – b2 = a2 – b2
See also removing brackets.
Examples
1. (2z – 5x)(2z + 5x) = (2z)2 – (5x)2 = 4z2 – 25x2
2. (3x + 4y)(3x – 4y) = (3x)2 – (4y)2 = 9x2 – 16y2
3. (12k – 14x)(12k + 14x) = (12k)2 – (14x)2 = 144k2 – 196x2