(3a-1/2)(3a-1/2) Using Identity

Jasonbradley

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Jun 16, 2024

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Expanding (3a - 1/2)(3a - 1/2) using the Identity

In mathematics, there are several identities that help simplify complex expressions. One of the most common is the square of a binomial identity:

(a - b)² = a² - 2ab + b²

We can use this identity to expand the expression (3a - 1/2)(3a - 1/2) which is equivalent to (3a - 1/2)².

Here's how:

1. Identify a and b: In this case, a = 3a and b = 1/2.

2. Substitute into the identity: (3a - 1/2)² = (3a)² - 2(3a)(1/2) + (1/2)²

3. Simplify: (3a)² - 2(3a)(1/2) + (1/2)² = 9a² - 3a + 1/4

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

Advantages of Using the Identity

Using the identity provides a more efficient way to expand the expression compared to direct multiplication:

• Reduced steps: The identity requires fewer steps than multiplying each term individually.
• Less prone to errors: Using the identity reduces the chances of making mistakes during multiplication.
• Clearer understanding: The identity helps to visualize the pattern of expansion and understand the resulting terms.

In summary, using the square of a binomial identity is a powerful tool for simplifying expressions and understanding the underlying mathematical concepts.