3(-2x+5)+(-2x+5)(x-3): Simplifying Algebraic Expressions
In this article, we will explore how to simplify the algebraic expression 3(-2x+5)+(-2x+5)(x-3). Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill to master.
Breaking Down the Expression
Let's break down the given expression into its components:
3(-2x+5): This is a term with a coefficient of 3, and a binomial expression-2x+5inside the parentheses.(-2x+5)(x-3): This is a product of two binomial expressions,-2x+5andx-3.
Simplifying the Expression
To simplify the expression, we will follow the order of operations (PEMDAS):
Step 1: Evaluate the expression inside the parentheses
3(-2x+5) = 3(-2x) + 3(5) = -6x + 15(-2x+5)(x-3) = -2x^2 + 6x - 15x + 45 = -2x^2 - 9x + 45
Step 2: Combine like terms
Now, we combine the two expressions:
-6x + 15 - 2x^2 - 9x + 45
Step 3: Simplify the expression
Combine like terms:
-2x^2 - 15x + 60
And that's the simplified expression!
Conclusion
In this article, we have successfully simplified the algebraic expression 3(-2x+5)+(-2x+5)(x-3) using the order of operations and combining like terms. The final simplified expression is -2x^2 - 15x + 60.
