(A + b)²
Understand the Problem
The question seems to be asking for the algebraic expansion of the expression (A + b)². This involves applying the formula for the square of a binomial.
Answer
The expanded form of $(A + b)^2$ is $A^2 + 2Ab + b^2$.
Answer for screen readers
The expanded form of the expression $(A + b)^2$ is $A^2 + 2Ab + b^2$.
Steps to Solve
- Identify the Binomial Expansion Formula
To expand the expression $(A + b)^2$, we can use the binomial expansion formula:
$$(x + y)^2 = x^2 + 2xy + y^2$$
In our case, $x = A$ and $y = b$.
- Substitute into the Formula
Now, substitute $A$ for $x$ and $b$ for $y$ in the formula:
$$(A + b)^2 = A^2 + 2Ab + b^2$$
- Write the Expanded Form
Combine the results from the substitution to write the expanded expression:
$$(A + b)^2 = A^2 + 2Ab + b^2$$
The expanded form of the expression $(A + b)^2$ is $A^2 + 2Ab + b^2$.
More Information
The expression $(A + b)^2$ is a classic example of a squared binomial, which is commonly encountered in algebra. It illustrates the distributive property and highlights the importance of recognizing patterns in algebraic expansions.
Tips
- Forget the middle term: A common mistake is to only write $A^2 + b^2$ and forget the $2Ab$ term. Remember that the middle term comes from multiplying both parts of the binomial.
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