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(1-4m)(m^2-3m+8)

3 min read Jun 16, 2024
(1-4m)(m^2-3m+8)

Expanding the Expression (1-4m)(m^2-3m+8)

This article will guide you through the process of expanding the algebraic expression (1-4m)(m^2-3m+8).

Understanding the Process

Expanding this expression involves multiplying each term in the first set of parentheses by each term in the second set of parentheses. This process is often referred to as FOIL (First, Outer, Inner, Last) when dealing with binomials, but it applies to any set of parentheses.

Step-by-Step Expansion

  1. Multiply the first terms of each set of parentheses: (1)(m^2) = m^2

  2. Multiply the outer terms of each set of parentheses: (1)(-3m) = -3m

  3. Multiply the inner terms of each set of parentheses: (-4m)(m^2) = -4m^3

  4. Multiply the last terms of each set of parentheses: (-4m)(-3m) = 12m^2

  5. Multiply the first term of the first set of parentheses by the last term of the second set of parentheses: (1)(8) = 8

  6. Multiply the last term of the first set of parentheses by the first term of the second set of parentheses: (-4m)(8) = -32m

  7. Combine all the terms: m^2 - 3m - 4m^3 + 12m^2 + 8 - 32m

  8. Rearrange the terms in descending order of their exponents: -4m^3 + m^2 + 12m^2 - 3m - 32m + 8

  9. Combine like terms: -4m^3 + 13m^2 - 35m + 8

Final Result

The expanded form of (1-4m)(m^2-3m+8) is -4m^3 + 13m^2 - 35m + 8.

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