Strange products » Square of sum
The rule:
(a + b)2 = a2 + 2ab + 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 + 2ab + b2
See also removing brackets.
Examples
1. (4x + 5)2 = (4x)2 + 2 · 4x · 5 + 52 = 16x2 + 40x + 25
2. (3z + 7)2 = (3z)2 + 2 · 3z · 7 + 72 = 9z2 + 42z + 49
3. (7x + 6y)2 = (7x)2 + 2 · 7x · 6y + (6y)2 = 49x2 + 84xy + 36y2