(x%2B6)%2B(x-1)(x%2B7).jpeg "(x+4)(x+6)+(x-1)(x+7)")
Expanding and Simplifying the Expression (x+4)(x+6)+(x-1)(x+7)
This article will guide you through the process of expanding and simplifying the expression (x+4)(x+6)+(x-1)(x+7).
Expanding the Expression
We will use the FOIL method to expand each of the products:
- First: Multiply the first terms of each binomial.
- Outer: Multiply the outer terms of each binomial.
- Inner: Multiply the inner terms of each binomial.
- Last: Multiply the last terms of each binomial.
Step 1: Expanding (x+4)(x+6)
- F: x * x = x²
- O: x * 6 = 6x
- I: 4 * x = 4x
- L: 4 * 6 = 24
Combining the terms, we get: x² + 6x + 4x + 24
Step 2: Expanding (x-1)(x+7)
- F: x * x = x²
- O: x * 7 = 7x
- I: -1 * x = -x
- L: -1 * 7 = -7
Combining the terms, we get: x² + 7x - x - 7
Combining the Expanded Terms
Now we have: (x² + 6x + 4x + 24) + (x² + 7x - x - 7)
Step 3: Combine like terms:
- x² + x² = 2x²
- 6x + 4x + 7x - x = 16x
- 24 - 7 = 17
Simplified Expression
The simplified expression is: 2x² + 16x + 17
Therefore, (x+4)(x+6)+(x-1)(x+7) = 2x² + 16x + 17