*(a-2b%2B3c-4d)-(-3)*(4a-3b%2B2c-d).jpeg "(-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.