What is the expansion of (a+b)^2?
Understand the Problem
The question is asking for the expansion of the algebraic expression (a+b)^2, which represents (a+b) multiplied by itself. The task is to provide the expanded form of this expression.
Answer
$a^2 + 2ab + b^2$
Answer for screen readers
$a^2 + 2ab + b^2$
Steps to Solve
- Write the expression as a product
$(a+b)^2$ is the same as $(a+b)(a+b)$.
- Apply the distributive property (FOIL method)
Multiply each term in the first parenthesis with each term in the second parenthesis:
$a * a + a * b + b * a + b * b$
- Simplify the terms
$a^2 + ab + ba + b^2$
- Combine like terms
Since $ab$ and $ba$ are the same, we can combine them:
$a^2 + 2ab + b^2$
$a^2 + 2ab + b^2$
More Information
The expansion of $(a+b)^2$ is a fundamental algebraic identity. It's a special case of the binomial theorem.
Tips
A common mistake is to assume that $(a+b)^2$ is equal to $a^2 + b^2$. The correct expansion includes the $2ab$ term. Forgetting this term leads to an incorrect simplification.
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