Binomial Formulas Explained Simply
The first binomial formula shows how to work out (a + b)² without just multiplying it out term by term. The colorful square below shows you exactly why it looks the way it does.
💬 Mia asks Grandpa Theo
Why isn't (a+b)² just a²+b²? That would be so much simpler!
A very common mistake! Look at the colorful square: next to the red a² field and the teal b² field, there are two golden ab rectangles - don't forget those!
And the second formula, (a-b)²?
Almost identical, just with a minus in front of the 2ab: (a-b)² = a² - 2ab + b². The b² stays positive though, since a square can never be negative.
And the third formula?
The third one is a special case: (a+b)(a-b) = a² - b². The mixed ab terms cancel each other out - look: +ab and -ab add up to zero!
Expand: (x + 3)²
Answer: x² + 6x + 9
Mental math trick: 102² = (100+2)² = 10000 + 400 + 4 = 10404 - no calculator needed!
Binomial formulas show up in almost every algebra problem from grade 8 onward - they're really worth memorizing.
← Back to overview