(x^2-4)(x+3)-(x^2+2x-5)

2 min read Jun 17, 2024
(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.