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

Jasonbradley

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Jun 16, 2024

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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.