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(2a-3b)^2

2 min read Jun 16, 2024
(2a-3b)^2

Expanding (2a-3b)^2

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

FOIL Method

FOIL stands for First, Outer, Inner, Last. It helps us multiply each term of the first binomial by each term of the second binomial:

  • First: (2a * 2a) = 4a^2
  • Outer: (2a * -3b) = -6ab
  • Inner: (-3b * 2a) = -6ab
  • Last: (-3b * -3b) = 9b^2

Adding all the terms together, we get: 4a^2 - 6ab - 6ab + 9b^2

Simplifying the expression, we get:

** (2a-3b)^2 = 4a^2 - 12ab + 9b^2 **

Square of a Binomial Formula

The square of a binomial formula is a shortcut for expanding expressions like (2a-3b)^2:

(a-b)^2 = a^2 - 2ab + b^2

Applying this formula to our expression:

  • a = 2a
  • b = 3b

Substituting the values in the formula:

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

Simplifying the expression, we get:

(2a-3b)^2 = 4a^2 - 12ab + 9b^2

Conclusion

Both methods lead to the same result: (2a-3b)^2 = 4a^2 - 12ab + 9b^2. The choice of method depends on personal preference and the complexity of the expression.

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