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.\n(2x)(x²)+(2x)(x)+(2x)(-2)+(3)(x²)+(3)(x)+(3)(-2)\nwhich is the simplified product?\n2x³ + 6x² - x - 6\n2x³ + x² - x - 6\n2x³ + 5x² - x - 6\n2x³ - x² - 7x - 6

using the distributive property, marta multiplied the binomial (2x + 3) by the trinomial (x² + x - 2) and got the expression below.\n(2x)(x²)+(2x)(x)+(2x)(-2)+(3)(x²)+(3)(x)+(3)(-2)\nwhich is the simplified product?\n2x³ + 6x² - x - 6\n2x³ + x² - x - 6\n2x³ + 5x² - x - 6\n2x³ - x² - 7x - 6

Answer

Explanation:

Step1: Expand each term

$(2x)(x^{2})=2x^{3}$, $(2x)(x) = 2x^{2}$, $(2x)(-2)=-4x$, $(3)(x^{2})=3x^{2}$, $(3)(x)=3x$, $(3)(-2)= - 6$.

Step2: Combine like - terms

The $x^{2}$ terms: $2x^{2}+3x^{2}=5x^{2}$; the $x$ terms: $-4x + 3x=-x$. The full expression is $2x^{3}+5x^{2}-x - 6$.

Answer:

$2x^{3}+5x^{2}-x - 6$