(x%2B3)-(x%5E2%2B2x-5).jpeg "(x^2-4)(x+3)-(x^2+2x-5)")
Simplifying the Expression: (x^2-4)(x+3)-(x^2+2x-5)
This article will guide you through the process of simplifying the algebraic expression: (x^2-4)(x+3)-(x^2+2x-5). We will break down the steps involved in order to arrive at a simplified form.
Step 1: Expanding the First Product
The first part of the expression involves multiplying two binomials: (x^2-4)(x+3). We can use the distributive property (or FOIL method) to expand this product:
- x^2 * x = x^3
- x^2 * 3 = 3x^2
- -4 * x = -4x
- -4 * 3 = -12
Combining these terms, we get: x^3 + 3x^2 - 4x - 12
Step 2: Simplifying the Entire Expression
Now we can rewrite the entire expression with the expanded product:
(x^3 + 3x^2 - 4x - 12) - (x^2 + 2x - 5)
Next, we distribute the negative sign in front of the second set of parentheses:
x^3 + 3x^2 - 4x - 12 - x^2 - 2x + 5
Step 3: Combining Like Terms
Finally, we combine the like terms to obtain the simplified expression:
x^3 + (3x^2 - x^2) + (-4x - 2x) + (-12 + 5)
This results in: x^3 + 2x^2 - 6x - 7
Conclusion
Therefore, the simplified form of the expression (x^2-4)(x+3)-(x^2+2x-5) is x^3 + 2x^2 - 6x - 7. This process demonstrates how to systematically simplify algebraic expressions through expansion and combining like terms.