Math Problem Statement

Use the distributive property to remove the parentheses: - (y - 4y - 1)

Solution

To remove the parentheses in the expression – (y – 4y – 1) using the distributive property, you distribute the –1 (negative sign) across each term inside the parentheses:

(y4y1)=1y+(1)(4y)+(1)(1)- (y - 4y - 1) = -1 \cdot y + (-1) \cdot (-4y) + (-1) \cdot (-1)

Simplify each term:

  1. -1 \cdot y = -y
  2. -1 \cdot (-4y) = +4y (negative times negative gives a positive)
  3. -1 \cdot (-1) = +1

Combine all terms:

y+4y+1- y + 4y + 1

Now simplify further by combining like terms (-y + 4y):

3y+13y + 1

Final Answer:

3y+13y + 1

Let me know if you want a deeper explanation or if you have other questions!


Here are 5 related questions to practice:

  1. Simplify: (2x5y+3)- (2x - 5y + 3)
  2. Apply the distributive property: (3a4b+7c)- (3a - 4b + 7c)
  3. Simplify: (6x2x8)- (6x - 2x - 8)
  4. Expand and simplify: (4m2n+5)- (4m - 2n + 5)
  5. Remove the parentheses: (x3x4y)- (x - 3x - 4y)

Tip:

When removing parentheses with a negative sign, distribute the –1 to each term inside the parentheses and carefully handle the signs.

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Math Problem Analysis

Mathematical Concepts

Algebra
Distributive Property
Simplifying Expressions

Formulas

Distributive Property: a(b + c) = ab + ac

Theorems

Distributive Property of Multiplication over Addition/Subtraction

Suitable Grade Level

Grades 6-8