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(v-5)(v+3)(v+2)

2 min read Jun 16, 2024
(v-5)(v+3)(v+2)

Factoring and Expanding (v-5)(v+3)(v+2)

This expression involves multiplying three binomials: (v-5), (v+3), and (v+2). We can solve this by following these steps:

Step 1: Multiply the first two binomials.

We can use the FOIL method to multiply (v-5) and (v+3):

  • First: v * v = v²
  • Outer: v * 3 = 3v
  • Inner: -5 * v = -5v
  • Last: -5 * 3 = -15

Combining the terms, we get: v² + 3v - 5v - 15 = v² - 2v - 15

Step 2: Multiply the result from step 1 with the remaining binomial.

Now we have to multiply (v² - 2v - 15) with (v+2). We can use the distributive property:

  • v² * (v + 2) = v³ + 2v²
  • -2v * (v + 2) = -2v² - 4v
  • -15 * (v + 2) = -15v - 30

Adding all the terms together: v³ + 2v² - 2v² - 4v - 15v - 30 = v³ - 19v - 30

Conclusion

Therefore, the expanded form of (v-5)(v+3)(v+2) is v³ - 19v - 30.

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