103k views
0 votes
Expand and simplify (5x+3)(3x-2)(x+3)

1 Answer

4 votes

Final answer:

To expand and simplify the expression (5x+3)(3x-2)(x+3), first multiply (5x+3) and (3x-2) to get 15x² - x - 6, and then multiply this by (x+3) to find the final expanded and simplified form, which is 15x³ + 44x² - 9x - 18.

Step-by-step explanation:

To expand and simplify the expression (5x+3)(3x-2)(x+3), we'll need to perform polynomial multiplication. First, we'll expand two of the three binomials, and then multiply the result by the remaining binomial. Here's how:

Multiply the first two binomials: (5x+3)(3x-2).

  • 5x * 3x = 15x²
  • 5x * (-2) = -10x
  • 3 * 3x = 9x
  • 3 * (-2) = -6

Combine like terms: 15x² - 10x + 9x - 6 = 15x² - x - 6.

Now multiply this trinomial by the remaining binomial (x+3).

  • (15x² - x - 6)(x + 3)
  • 15x² * x = 15x³
  • 15x² * 3 = 45x²
  • -x * x = -x²
  • -x * 3 = -3x
  • -6 * x = -6x
  • -6 * 3 = -18

Combine all the like terms to get the final expanded form: 15x³ + 45x² - x² - 3x - 6x - 18.

Simplify: 15x³ + 44x² - 9x - 18.

User Shmck
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories