(-5)*(a-2b+3c-4d)-(-3)*(4a-3b+2c-d)

2 min read Jun 16, 2024
(-5)*(a-2b+3c-4d)-(-3)*(4a-3b+2c-d)

Simplifying Algebraic Expressions: A Step-by-Step Guide

This article will guide you through the process of simplifying the algebraic expression: (-5)(a-2b+3c-4d)-(-3)(4a-3b+2c-d). We'll break down each step to ensure a clear understanding.

Step 1: Distribute the Multipliers

First, we need to distribute the multipliers (-5) and (-3) across the parentheses. This involves multiplying each term inside the parentheses by the corresponding multiplier:

  • (-5)*(a-2b+3c-4d) becomes -5a + 10b - 15c + 20d
  • (-3)*(4a-3b+2c-d) becomes -12a + 9b - 6c + 3d

Step 2: Combine Like Terms

Now we have: -5a + 10b - 15c + 20d - (-12a + 9b - 6c + 3d)

Next, we combine like terms. This means grouping terms with the same variable and exponent together:

  • -5a + 12a = 7a
  • 10b - 9b = b
  • -15c + 6c = -9c
  • 20d - 3d = 17d

Step 3: Final Result

Finally, we combine all the simplified terms to get the final result:

7a + b - 9c + 17d

Therefore, the simplified form of the expression (-5)(a-2b+3c-4d)-(-3)(4a-3b+2c-d) is 7a + b - 9c + 17d.

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