(1/2x+4/3)(1/2x-4/3)

Jasonbradley

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Jun 16, 2024

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Expanding and Simplifying (1/2x + 4/3)(1/2x - 4/3)

This expression is in the form of a difference of squares, which has a specific pattern that makes it easier to expand.

Understanding the Pattern:

The difference of squares pattern states that:

(a + b)(a - b) = a² - b²

Applying the Pattern:

In our case:

• a = 1/2x
• b = 4/3

Therefore, we can directly apply the pattern:

(1/2x + 4/3)(1/2x - 4/3) = (1/2x)² - (4/3)²

Simplifying:

• (1/2x)² = (1/2)² * x² = 1/4x²
• (4/3)² = 16/9

So, the expanded and simplified form is:

1/4x² - 16/9

Conclusion:

By recognizing the difference of squares pattern, we could efficiently expand and simplify the expression (1/2x + 4/3)(1/2x - 4/3) to 1/4x² - 16/9.