https://file.aiquickdraw.com/mathbot/file/17273455982555tz5wc60.jpg

The image contains three expressions involving binomials raised to powers:

1. \((a + b)^2\)
2. \((a + b)^3\)
3. \((a + b)^4\)

Let's expand each expression using the binomial theorem or direct multiplication.

### 1. Expansion of \((a + b)^2\):
\[
(a + b)^2 = (a + b)(a + b) = a^2 + 2ab + b^2
\]

### 2. Expansion of \((a + b)^3\):
\[
(a + b)^3 = (a + b)(a + b)(a + b) = a^3 + 3a^2b + 3ab^2 + b^3
\]

### 3. Expansion of \((a + b)^4\):
\[
(a + b)^4 = (a + b)(a + b)(a + b)(a + b) = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4
\]

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Would you like further details or have any questions about these expansions?

Here are some related questions to consider:
1. How can the binomial theorem be generalized for any power \( n \)?
2. What are the coefficients in each term of a binomial expansion, and how are they determined?
3. Can you apply Pascal’s Triangle to find the coefficients of the binomial expansion?
4. How can these expansions be used to solve problems in algebra and calculus?
5. What happens if the terms \( a \) and \( b \) in the binomial are complex numbers?

**Tip:** The binomial expansion can be used to approximate powers of numbers close to 1 by choosing \( a = 1 \) and \( b = x \), where \( x \) is small.

Expand (a + b)^2, (a + b)^3, and (a + b)^4.

Expand the binomials (a + b)^2, (a + b)^3, and (a + b)^4 step-by-step using the binomial theorem. Learn how to apply algebraic concepts like binomial expansion and Pascal’s Triangle. Suitable for students in Grades 9-12.

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