(4y%5E2-y-7).jpeg "(-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.
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Distribute the first term of the first binomial (-3y) over the second binomial: (-3y)(4y² - y - 7) = -12y³ + 3y² + 21y
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Distribute the second term of the first binomial (+1) over the second binomial: (1)(4y² - y - 7) = 4y² - y - 7
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Combine the results from steps 1 and 2: -12y³ + 3y² + 21y + 4y² - y - 7
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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.