(3a2-%2B-7xy).jpeg "(3a2 - 7xy)(3a2 + 7xy)")
Understanding the Special Product: (3a² - 7xy)(3a² + 7xy)
This expression represents a special product known as the difference of squares. It follows the pattern:
(a - b)(a + b) = a² - b²
Let's break down how to apply this pattern to the given expression:
1. Identify 'a' and 'b'
- In our case, a = 3a² and b = 7xy.
2. Apply the Difference of Squares Formula
- Substitute the values of 'a' and 'b' into the formula: (3a² - 7xy)(3a² + 7xy) = (3a²)² - (7xy)²
3. Simplify
- Square the terms: 9a⁴ - 49x²y²
Therefore, the simplified form of (3a² - 7xy)(3a² + 7xy) is 9a⁴ - 49x²y².
Understanding the Importance of Recognizing Special Products
Recognizing special products like the difference of squares is crucial in simplifying algebraic expressions. It allows you to:
- Quickly expand expressions: Instead of multiplying each term individually, you can directly apply the formula.
- Factorize expressions efficiently: You can use the pattern to factor expressions into simpler forms.
- Solve equations more easily: By recognizing special products, you can manipulate equations to simplify them and find solutions.
In conclusion, by understanding the difference of squares formula, you can efficiently simplify expressions like (3a² - 7xy)(3a² + 7xy) and streamline your algebraic work.