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Expanding the Expression: (2x-9)(x+5)
This article will guide you through the process of expanding the expression (2x-9)(x+5). This is a fundamental concept in algebra, involving the multiplication of two binomials.
Understanding the Concept
When multiplying binomials, we use the distributive property. This means we multiply each term in the first binomial by each term in the second binomial.
Expanding the Expression
Let's break down the expansion:
- Step 1: Multiply the first term of the first binomial (2x) by each term in the second binomial:
- (2x) * (x) = 2x²
- (2x) * (5) = 10x
- Step 2: Multiply the second term of the first binomial (-9) by each term in the second binomial:
- (-9) * (x) = -9x
- (-9) * (5) = -45
Combining Like Terms
Now, we have the following terms: 2x², 10x, -9x, and -45. We can combine the like terms (10x and -9x):
- 2x² + 10x - 9x - 45
Simplified Expression
Finally, the expanded and simplified form of the expression (2x-9)(x+5) is:
2x² + x - 45
Conclusion
By applying the distributive property and combining like terms, we successfully expanded the expression (2x-9)(x+5) to its simplified form, 2x² + x - 45. This process is essential for manipulating and solving various algebraic equations and expressions.