using the distributive property, marta multiplied the binomial (2x + 3) by the trinomial (x² + x - 2) and…

using the distributive property, marta multiplied the binomial (2x + 3) by the trinomial (x² + x - 2) and got the expression below. (2x)(x²) + (2x)(x) + (2x)(-2) + (3)(x²) + (3)(x) + (3)(-2) which is the simplified product? 2x³ + 6x² - x - 6 2x³ + x² - x - 6 2x³ + 5x² - x - 6 2x³ - x² - 7x - 6

using the distributive property, marta multiplied the binomial (2x + 3) by the trinomial (x² + x - 2) and got the expression below. (2x)(x²) + (2x)(x) + (2x)(-2) + (3)(x²) + (3)(x) + (3)(-2) which is the simplified product? 2x³ + 6x² - x - 6 2x³ + x² - x - 6 2x³ + 5x² - x - 6 2x³ - x² - 7x - 6

Answer

Explanation:

Step1: Simplify each term

  • For ((2x)(x^{2})), using the rule (a^m\times a^n=a^{m + n}), we get (2x^{3}).
  • For ((2x)(x)), we have (2x^{2}).
  • For ((2x)(-2)), it is (-4x).
  • For ((3)(x^{2})), we get (3x^{2}).
  • For ((3)(x)), it is (3x).
  • For ((3)(-2)), we have (-6).

The expression becomes (2x^{3}+2x^{2}-4x + 3x^{2}+3x-6).

Step2: Combine like - terms

  • Combine the (x^{2}) terms: (2x^{2}+3x^{2}=5x^{2}).
  • Combine the (x) terms: (-4x + 3x=-x).

The simplified product is (2x^{3}+5x^{2}-x - 6).

Answer:

(2x^{3}+5x^{2}-x - 6) (the third option)