(-3y+1)(4y^2-y-7)

2 min read Jun 16, 2024
(-3y+1)(4y^2-y-7)

Expanding the Expression (-3y + 1)(4y² - y - 7)

This article will guide you through the process of expanding the expression (-3y + 1)(4y² - y - 7).

Understanding the Problem

We are given a product of two binomials:

  • (-3y + 1)
  • (4y² - y - 7)

Our goal is to multiply these binomials to obtain a simplified polynomial expression.

Applying the Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each term of the sum by that number. We can use this property to expand the given expression.

  1. Distribute the first term of the first binomial (-3y) over the second binomial: (-3y)(4y² - y - 7) = -12y³ + 3y² + 21y

  2. Distribute the second term of the first binomial (+1) over the second binomial: (1)(4y² - y - 7) = 4y² - y - 7

  3. Combine the results from steps 1 and 2: -12y³ + 3y² + 21y + 4y² - y - 7

  4. Simplify by combining like terms: -12y³ + 7y² + 20y - 7

Final Answer

Therefore, the expanded form of (-3y + 1)(4y² - y - 7) is -12y³ + 7y² + 20y - 7.

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