(ab+3)^2

Jasonbradley

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Jun 16, 2024

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Expanding (ab + 3)^2

The expression (ab + 3)^2 represents the square of the binomial (ab + 3). To expand this expression, we can utilize the FOIL method, which stands for First, Outer, Inner, Last.

Here's how to expand the expression:

1. First: Multiply the first terms of each binomial: (ab) * (ab) = a²b²
2. Outer: Multiply the outer terms of the binomials: (ab) * (3) = 3ab
3. Inner: Multiply the inner terms of the binomials: (3) * (ab) = 3ab
4. Last: Multiply the last terms of each binomial: (3) * (3) = 9

Now, add all the results together:

a²b² + 3ab + 3ab + 9

Finally, combine the like terms:

a²b² + 6ab + 9

Therefore, the expanded form of (ab + 3)^2 is a²b² + 6ab + 9.

Understanding the Process

Expanding (ab + 3)^2 is essentially multiplying the binomial by itself:

(ab + 3)^2 = (ab + 3)(ab + 3)

The FOIL method helps us systematically multiply each term in the first binomial with each term in the second binomial.

Alternative Methods

While the FOIL method is commonly used, there are alternative approaches to expanding binomials:

• Using the distributive property: We can distribute (ab + 3) over itself, resulting in the same expanded form.
• Using the binomial theorem: For higher powers of binomials, the binomial theorem provides a more efficient way to expand the expression.

Key takeaways

• The FOIL method is a straightforward way to expand binomials.
• Understanding the process of expanding binomials is crucial for simplifying algebraic expressions and solving equations.
• Exploring alternative methods like the distributive property and the binomial theorem can offer different perspectives on expanding binomials.