(1%2Bx)-3(5-2x).jpeg "(2-x)(1+x)-3(5-2x)")
Simplifying the Expression (2-x)(1+x)-3(5-2x)
This article will guide you through the process of simplifying the algebraic expression: (2-x)(1+x)-3(5-2x).
Step 1: Expand the Products
We begin by expanding the products using the distributive property:
- (2-x)(1+x):
- 2(1+x) - x(1+x)
- 2 + 2x - x - x²
- 2 + x - x²
- 3(5-2x):
- 15 - 6x
Now, our expression looks like this: (2 + x - x²) - (15 - 6x)
Step 2: Combine Like Terms
Next, we remove the parentheses and combine the like terms:
- 2 + x - x² - 15 + 6x
- -x² + 7x - 13
Final Simplified Expression
Therefore, the simplified form of the expression (2-x)(1+x)-3(5-2x) is -x² + 7x - 13.
Conclusion
By applying the distributive property and combining like terms, we successfully simplified the given expression. This process is crucial in algebra, allowing us to manipulate and solve equations more effectively.