(x%2B5)-(x%2B5)(2x-4).jpeg "(3x+7)(x+5)-(x+5)(2x-4)")
Simplifying the Expression (3x+7)(x+5)-(x+5)(2x-4)
This article will guide you through the process of simplifying the algebraic expression (3x+7)(x+5)-(x+5)(2x-4).
Step 1: Expanding the Expressions
We begin by expanding each of the products using the distributive property (also known as FOIL method):
- (3x+7)(x+5)
- = 3x(x+5) + 7(x+5)
- = 3x² + 15x + 7x + 35
- = 3x² + 22x + 35
- (x+5)(2x-4)
- = x(2x-4) + 5(2x-4)
- = 2x² - 4x + 10x - 20
- = 2x² + 6x - 20
Step 2: Combining the Expanded Expressions
Now, we substitute the expanded expressions back into the original equation:
- (3x² + 22x + 35) - (2x² + 6x - 20)
Remember to distribute the negative sign:
- 3x² + 22x + 35 - 2x² - 6x + 20
Step 3: Combining Like Terms
Finally, we combine the like terms to simplify the expression:
- (3x² - 2x²) + (22x - 6x) + (35 + 20)
- x² + 16x + 55
Conclusion
Therefore, the simplified form of the expression (3x+7)(x+5)-(x+5)(2x-4) is x² + 16x + 55. This process demonstrates the importance of understanding the distributive property and combining like terms to simplify complex algebraic expressions.