(a+b)^2
Understand the Problem
The question is presenting a mathematical expression, specifically a binomial expression raised to the power of 2. We need to simplify or expand the expression using algebraic identities.
Answer
The expanded form is $a^2 + 2ab + b^2$.
Answer for screen readers
The simplified expression for $(a + b)^2$ is $a^2 + 2ab + b^2$.
Steps to Solve
- Identify the binomial expression
First, we need to recognize the binomial expression we are working with. Let's say the expression is $(a + b)^2$.
- Apply the binomial theorem
According to the binomial theorem, the expansion of $(a + b)^2$ can be calculated using the formula:
$$(a + b)^2 = a^2 + 2ab + b^2$$
- Substitute and simplify
Now we will substitute the values of $a$ and $b$ if they are given; otherwise, we will leave the terms as is. For example, if $a = 3$ and $b = 2$, we would have:
$$ (3 + 2)^2 = 3^2 + 2(3)(2) + 2^2 $$
- Calculate each term
Calculate each term in the expression:
- $3^2 = 9$
- $2(3)(2) = 12$
- $2^2 = 4$
- Combine the results
Finally, we will combine these results together:
$$ 9 + 12 + 4 = 25 $$
The simplified expression for $(a + b)^2$ is $a^2 + 2ab + b^2$.
More Information
This expansion is useful for various algebraic applications and helps in polynomial multiplication. Knowing this expansion also aids in factoring quadratic equations.
Tips
- Forgetting to include the $2ab$ term in the expansion.
- Confusing the binomial expansion with other types (like perfect squares). It's important to remember the specific formula for binomials.
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