and-4(a%5E2-2%2F3b%5E2).jpeg "(3/4a^2+3b^2)and 4(a^2-2/3b^2)")
Simplifying Algebraic Expressions: (3/4a^2 + 3b^2) and 4(a^2 - 2/3b^2)
In mathematics, simplifying expressions is a fundamental skill. It involves manipulating expressions to make them easier to understand and work with. Today, we'll focus on simplifying two expressions: (3/4a^2 + 3b^2) and 4(a^2 - 2/3b^2).
Simplifying (3/4a^2 + 3b^2)
This expression involves adding two terms. Since the terms have different variables, we cannot combine them directly. However, we can simplify the expression by factoring out a common factor:
1. Find the Greatest Common Factor (GCF): The GCF of 3/4 and 3 is 3/4.
2. Factor out the GCF: (3/4a^2 + 3b^2) = (3/4)(a^2 + 4b^2)
Therefore, the simplified expression is (3/4)(a^2 + 4b^2).
Simplifying 4(a^2 - 2/3b^2)
This expression involves a constant factor multiplied by a binomial. To simplify it, we need to distribute the constant factor:
1. Distribute the constant factor (4): 4(a^2 - 2/3b^2) = 4a^2 - 8/3b^2
Therefore, the simplified expression is 4a^2 - 8/3b^2.
Summary
In conclusion, we successfully simplified both expressions:
- (3/4a^2 + 3b^2) simplifies to (3/4)(a^2 + 4b^2)
- 4(a^2 - 2/3b^2) simplifies to 4a^2 - 8/3b^2
Simplifying expressions is an important process that allows us to work more efficiently with algebraic expressions. By understanding how to factor, distribute, and combine terms, we can make complex expressions easier to handle.