(a-2)-(a-5)(a%2B3).jpeg "(a-1)(a-2)-(a-5)(a+3)")
(a-1)(a-2)-(a-5)(a+3): The Art of Expanding and Simplifying Algebraic Expressions
Algebraic expressions are a fundamental part of mathematics, and understanding how to expand and simplify them is crucial for problem-solving. In this article, we'll explore the expression (a-1)(a-2)-(a-5)(a+3), breaking it down into its components and simplifying it step by step.
Expanding the Expression
To simplify the expression (a-1)(a-2)-(a-5)(a+3), we need to start by expanding each set of parentheses.
(a-1)(a-2) = ?
To expand (a-1)(a-2), we'll multiply each term in the first set of parentheses by each term in the second set:
(a-1)(a-2) = a(a-2) - 1(a-2)
= a^2 - 2a - a + 2
= a^2 - 3a + 2
(a-5)(a+3) = ?
Next, let's expand (a-5)(a+3):
(a-5)(a+3) = a(a+3) - 5(a+3)
= a^2 + 3a - 5a - 15
= a^2 - 2a - 15
Simplifying the Expression
Now that we've expanded both sets of parentheses, we can simplify the entire expression:
(a-1)(a-2)-(a-5)(a+3) = (a^2 - 3a + 2) - (a^2 - 2a - 15)
= a^2 - 3a + 2 - a^2 + 2a + 15
= **-a + 17**
Conclusion
And there you have it! By expanding and simplifying the expression (a-1)(a-2)-(a-5)(a+3), we've arrived at the simplified form -a + 17. This exercise demonstrates the importance of following the order of operations (PEMDAS) and being mindful of the signs when expanding and simplifying algebraic expressions.
