(x%2B7)-1%2F4x%5E2.jpeg "(3x-4)(x+7)-1/4x^2")
Simplifying the Expression (3x-4)(x+7) - 1/4x^2
This article will guide you through the process of simplifying the algebraic expression (3x-4)(x+7) - 1/4x^2. We'll break down the steps involved, making it easy to understand.
Step 1: Expanding the Product
The first part of the expression is a product of two binomials: (3x-4)(x+7). To simplify this, we can use the FOIL method:
- First: 3x * x = 3x²
- Outer: 3x * 7 = 21x
- Inner: -4 * x = -4x
- Last: -4 * 7 = -28
Adding these terms together gives us: 3x² + 21x - 4x - 28.
Step 2: Combining Like Terms
Now we can combine the terms with 'x' in them: 3x² + (21x - 4x) - 28 = 3x² + 17x - 28.
Step 3: Subtracting the Fractional Term
We need to subtract 1/4x² from the expression we've simplified so far. Since this is a single term, we can simply write it next to the other terms: 3x² + 17x - 28 - 1/4x².
Step 4: Combining Like Terms (Again)
Finally, we can combine the x² terms: (3 - 1/4)x² + 17x - 28.
The Simplified Expression
After completing all the steps, the simplified form of the expression is: (11/4)x² + 17x - 28.
This is the simplest form of the original expression. It is important to note that there are often different ways to simplify expressions, but they will all result in equivalent forms.