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(6v2+2v−9)(4−5v)

less than a minute read Jun 16, 2024
(6v2+2v−9)(4−5v)

Expanding the Expression: (6v² + 2v - 9)(4 - 5v)

This expression involves multiplying two binomials, one of which is a trinomial. To expand this, we'll use the distributive property (also known as FOIL - First, Outer, Inner, Last) for each term in the first binomial with each term in the second binomial.

Here's how to break it down step-by-step:

  1. Distribute the 6v²:

    • (6v²) * (4) = 24v²
    • (6v²) * (-5v) = -30v³

  2. Distribute the 2v:

    • (2v) * (4) = 8v
    • (2v) * (-5v) = -10v²

  3. Distribute the -9:

    • (-9) * (4) = -36
    • (-9) * (-5v) = 45v

  4. Combine all the terms:

    • 24v² - 30v³ + 8v - 10v² - 36 + 45v

  5. Simplify by combining like terms:

    • -30v³ + 14v² + 53v - 36

Therefore, the expanded form of (6v² + 2v - 9)(4 - 5v) is -30v³ + 14v² + 53v - 36.

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