(2u+3)(u-4)+4u(u-2)

2 min read Jun 16, 2024
(2u+3)(u-4)+4u(u-2)

Simplifying Algebraic Expressions: (2u+3)(u-4)+4u(u-2)

This article will guide you through the process of simplifying the algebraic expression (2u+3)(u-4)+4u(u-2). We'll use the distributive property and combine like terms to reach a simplified form.

Step 1: Distribute

First, we apply the distributive property to expand the expressions within the parentheses.

  • For (2u+3)(u-4), we multiply each term in the first parenthesis by each term in the second:

    • (2u)(u) = 2u²
    • (2u)(-4) = -8u
    • (3)(u) = 3u
    • (3)(-4) = -12
  • For 4u(u-2), we multiply each term in the parenthesis by 4u:

    • (4u)(u) = 4u²
    • (4u)(-2) = -8u

Step 2: Combine Like Terms

Now, we add all the resulting terms and combine those with the same variable and exponent:

(2u² - 8u + 3u - 12) + (4u² - 8u)

Combining like terms:

  • 2u² + 4u² = 6u²
  • -8u + 3u - 8u = -13u
  • -12 remains as a constant term

Simplified Expression

After simplifying, the expression becomes:

6u² - 13u - 12

This is the simplified form of the original algebraic expression.

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