Jasonbradley
Home

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

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

Simplifying Algebraic Expressions

This article will guide you through the process of simplifying the algebraic expression: (-5)x(a-2b+3c-4d)-(-3)x(4a-3b+2c-d)

Understanding the Steps

  1. Distribute: We begin by distributing the scalar values (-5) and (-3) to each term inside the parentheses. This involves multiplying each term within the parentheses by the scalar.

  2. Simplify: After distributing, we combine like terms. This means adding or subtracting terms that have the same variables and exponents.

Step-by-Step Solution

Let's break down the simplification process step-by-step:

  1. Distribute:

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

  2. Combine Like Terms:

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

  3. Simplify:

    • -17a + 19b - 21c + 23d

Final Answer

The simplified form of the expression (-5)x(a-2b+3c-4d)-(-3)x(4a-3b+2c-d) is -17a + 19b - 21c + 23d.

Key Takeaways

  • Distribution: When multiplying a scalar by an expression within parentheses, remember to multiply each term inside the parentheses by the scalar.
  • Combining Like Terms: This simplifies the expression by grouping terms with the same variable and exponent.

This process of simplifying algebraic expressions is fundamental in algebra and is crucial for solving equations and manipulating formulas.

Related Post

Featured Posts