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?\n○ 2x³ + 6x² - x - 6\n○ 2x³ + x² - x - 6\n○ 2x³ + 5x² - x - 6\n○ 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.\n(2x)(x²)+(2x)(x)+(2x)(-2)+(3)(x²)+(3)(x)+(3)(-2)\nwhich is the simplified product?\n○ 2x³ + 6x² - x - 6\n○ 2x³ + x² - x - 6\n○ 2x³ + 5x² - x - 6\n○ 2x³ - x² - 7x - 6

Answer

Explanation:

Step1: Multiply 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 are $2x^{2}$ and $3x^{2}$, so $2x^{2}+3x^{2}=5x^{2}$. The $x$ terms are $-4x$ and $3x$, so $-4x + 3x=-x$. The resulting polynomial is $2x^{3}+5x^{2}-x - 6$.

Answer:

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