Expand the expression (A+b)².
Understand the Problem
The question presents the expression (A+b)², which represents the square of a binomial. The user likely wants to expand this expression using the distributive property or the binomial theorem.
Answer
$A^2 + 2Ab + b^2$
Answer for screen readers
$A^2 + 2Ab + b^2$
Steps to Solve
- Write out the expression
To expand $(A+b)^2$, we can rewrite it as the product $(A+b)(A+b)$.
- Apply the distributive property (also known as FOIL)
Multiply each term in the first binomial by each term in the second binomial: $$(A+b)(A+b) = A \cdot A + A \cdot b + b \cdot A + b \cdot b$$
- Simplify the expression
Combine like terms: $$A^2 + Ab + bA + b^2 = A^2 + Ab + Ab + b^2$$ $$A^2 + 2Ab + b^2$$
$A^2 + 2Ab + b^2$
More Information
The expansion of $(A+b)^2$ is a common algebraic identity. It appears frequently, especially in algebra and calculus. It's also a specific case of the binomial theorem.
Tips
A common mistake is to incorrectly expand $(A+b)^2$ as $A^2 + b^2$. The middle term, $2Ab$, is often missed. Remember that $(A+b)^2 = (A+b)(A+b)$, and you need to apply the distributive property (FOIL) correctly.
AI-generated content may contain errors. Please verify critical information
