(x%2B7).jpeg "(2x-5)(x+7)")
Expanding and Simplifying (2x-5)(x+7)
This article explores how to expand and simplify the expression (2x-5)(x+7). This process involves using the distributive property, also known as FOIL (First, Outer, Inner, Last).
Expanding using FOIL
- First: Multiply the first terms of each binomial: 2x * x = 2x²
- Outer: Multiply the outer terms of each binomial: 2x * 7 = 14x
- Inner: Multiply the inner terms of each binomial: -5 * x = -5x
- Last: Multiply the last terms of each binomial: -5 * 7 = -35
Now we have: 2x² + 14x - 5x - 35
Simplifying
Combine the like terms (the terms with x): 2x² + 9x - 35
Therefore, the expanded and simplified form of (2x-5)(x+7) is 2x² + 9x - 35.
Understanding the result
The expanded form 2x² + 9x - 35 represents a quadratic expression. This expression represents a parabola when graphed, and its roots (where the graph intersects the x-axis) can be found by solving the equation 2x² + 9x - 35 = 0.