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(2a+3b)2 Answer

2 min read Jun 16, 2024
(2a+3b)2 Answer

Expanding the Square: (2a + 3b)2

The expression (2a + 3b)2 represents the square of the binomial (2a + 3b). To expand this, we can use the FOIL method or the square of a binomial formula.

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last. This method helps us multiply each term in the first binomial with each term in the second binomial:

  1. First: Multiply the first terms of each binomial: (2a) * (2a) = 4a²
  2. Outer: Multiply the outer terms: (2a) * (3b) = 6ab
  3. Inner: Multiply the inner terms: (3b) * (2a) = 6ab
  4. Last: Multiply the last terms: (3b) * (3b) = 9b²

Now, combine all the terms: 4a² + 6ab + 6ab + 9b²

Finally, simplify by combining like terms: 4a² + 12ab + 9b²

Using the Square of a Binomial Formula

The square of a binomial formula states: (a + b)² = a² + 2ab + b²

In our case, a = 2a and b = 3b. Let's apply the formula:

(2a + 3b)² = (2a)² + 2(2a)(3b) + (3b)²

Simplifying, we get: 4a² + 12ab + 9b²

Conclusion

Both methods lead to the same expanded form: 4a² + 12ab + 9b². Remember to distribute the exponent to both terms within the parentheses and pay attention to the signs when combining like terms.

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