#1
Top 50 Mistake
Thinking $(a + b)^2 = a^2 + b^2$
"The Binomial Blunder"
The Mistake in Action
Expand $(x + 3)^2$
Wrong: $x^2 + 9$
Why It Happens
Students "distribute" the square to each term inside, treating the brackets like multiplication distributes. But squaring is not multiplication by a number — $(x+3)^2$ means $(x+3)(x+3)$.
The Fix
$(x + 3)^2$ means $(x + 3)(x + 3)$
Use FOIL or remember the pattern: $$(a + b)^2 = a^2 + 2ab + b^2$$
Expanding: $$(x + 3)(x + 3) = x^2 + 3x + 3x + 9 = x^2 + 6x + 9$$
The middle term (2ab = 6x) is what's missing!
Spot the Mistake
Can you identify where this student went wrong?
Expand $(x + 3)^2$
$= x^2 + 9$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: