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(x^3+3x^2-2x+5)(x-7)

2 min read Jun 17, 2024
(x^3+3x^2-2x+5)(x-7)

Expanding the Expression: (x^3 + 3x^2 - 2x + 5)(x - 7)

This article will guide you through the process of expanding the given expression: (x^3 + 3x^2 - 2x + 5)(x - 7). This involves multiplying each term within the first set of parentheses by each term in the second set of parentheses.

Applying the Distributive Property

We will apply the distributive property twice to expand this expression. This means we'll multiply each term in the first set of parentheses by x and then by -7.

Let's break down the steps:

Step 1: Multiply each term in the first set of parentheses by x:

  • x^3 * x = x^4
  • 3x^2 * x = 3x^3
  • -2x * x = -2x^2
  • 5 * x = 5x

Step 2: Multiply each term in the first set of parentheses by -7:

  • x^3 * -7 = -7x^3
  • 3x^2 * -7 = -21x^2
  • -2x * -7 = 14x
  • 5 * -7 = -35

Combining Like Terms

Now, we combine the terms we obtained in the previous steps, remembering to pay attention to the signs:

  • x^4
  • 3x^3 - 7x^3 = -4x^3
  • -2x^2 - 21x^2 = -23x^2
  • 5x + 14x = 19x
  • -35

Final Expanded Expression

Therefore, the expanded form of the expression (x^3 + 3x^2 - 2x + 5)(x - 7) is:

x^4 - 4x^3 - 23x^2 + 19x - 35

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