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Simplifying Algebraic Expressions: (3a - 7b)² - 42ab
This article will guide you through simplifying the algebraic expression (3a - 7b)² - 42ab. We will use the concepts of FOIL method and combining like terms to reach the solution.
Understanding the Expression
The expression consists of two parts:
- (3a - 7b)²: This is a binomial squared.
- - 42ab: This is a simple term with coefficients and variables.
Applying the FOIL Method
The FOIL method helps us expand the square of a binomial:
First: (3a * 3a) = 9a² Outer: (3a * -7b) = -21ab Inner: (-7b * 3a) = -21ab Last: (-7b * -7b) = 49b²
Therefore, (3a - 7b)² expands to 9a² - 21ab - 21ab + 49b²
Combining Like Terms
Now, let's combine the like terms in the expanded expression:
9a² - 21ab - 21ab + 49b² - 42ab = 9a² - 84ab + 49b²
Final Solution
The simplified form of the expression (3a - 7b)² - 42ab is 9a² - 84ab + 49b².
Key Takeaways
- The FOIL method is crucial for expanding binomials.
- Identifying and combining like terms simplifies expressions.
- Algebraic expressions can be simplified to make them easier to understand and manipulate.