(x%2B3)%2B(x-2)(x%2B8).jpeg "(x+5)(x+3)+(x-2)(x+8)")
Expanding and Simplifying the Expression (x+5)(x+3)+(x-2)(x+8)
This article will guide you through the process of expanding and simplifying the algebraic expression (x+5)(x+3)+(x-2)(x+8).
Understanding the Expression
The expression consists of two separate multiplications:
- (x+5)(x+3)
- (x-2)(x+8)
These multiplications are then added together.
Expanding the Multiplications
We will use the FOIL method to expand each multiplication:
- 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.
For (x+5)(x+3):
- First: x * x = x²
- Outer: x * 3 = 3x
- Inner: 5 * x = 5x
- Last: 5 * 3 = 15
Combining these terms, we get: x² + 3x + 5x + 15
For (x-2)(x+8):
- First: x * x = x²
- Outer: x * 8 = 8x
- Inner: -2 * x = -2x
- Last: -2 * 8 = -16
Combining these terms, we get: x² + 8x - 2x - 16
Combining the Expanded Expressions
Now we have:
(x² + 3x + 5x + 15) + (x² + 8x - 2x - 16)
To simplify, we combine like terms:
- x² + x² = 2x²
- 3x + 5x + 8x - 2x = 14x
- 15 - 16 = -1
Final Simplified Expression
The simplified form of the expression (x+5)(x+3)+(x-2)(x+8) is:
2x² + 14x - 1