(3a-1/2)(3a-1/2) Solution

Jasonbradley

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Jun 16, 2024

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Solving (3a - 1/2)(3a - 1/2)

This expression represents the square of the binomial (3a - 1/2). We can solve this by using the FOIL method or by applying the square of a binomial formula.

Using FOIL Method

FOIL stands for First, Outer, Inner, Last. It helps us multiply two binomials systematically.

1. First: Multiply the first terms of each binomial: 3a * 3a = 9a²
2. Outer: Multiply the outer terms of the binomials: 3a * (-1/2) = -3/2a
3. Inner: Multiply the inner terms of the binomials: (-1/2) * 3a = -3/2a
4. Last: Multiply the last terms of each binomial: (-1/2) * (-1/2) = 1/4

Now, combine all the terms:

9a² - 3/2a - 3/2a + 1/4

Simplify the expression by combining like terms:

9a² - 3a + 1/4

Using the Square of a Binomial Formula

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

1. Identify 'a' and 'b':
   • a = 3a
   • b = 1/2
2. Apply the formula:
   • (3a)² - 2(3a)(1/2) + (1/2)²
3. Simplify the expression:
   • 9a² - 3a + 1/4

Therefore, the solution of (3a - 1/2)(3a - 1/2) is 9a² - 3a + 1/4.