Question

using the distributive property, marta multiplied the binomial $(2x + 3)$ by the trinomial $(x^{2}+x - 2)$ and got the given expression.$(2x)(x^{2})+(2x)(x)+(2x)(-2)+(3)(x^{2})+(3)(x)+(3)(-2)$which is the simplified product?$2x^{3}-x^{2}-7x - 6LXB02x^{3}+x^{2}-x - 6$

Explanation:

Step1: Calculate 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 all terms

$2x^3 + 2x^2 - 4x + 3x^2 + 3x - 6$

Step3: Combine like terms

$2x^3 + (2x^2+3x^2) + (-4x+3x) - 6 = 2x^3 + 5x^2 - x - 6$
(Note: There is a discrepancy with the provided options; the correct simplified product derived from the expanded form is $2x^3 + 5x^2 - x - 6$. If we assume a typo in the second option's $6x^2$ should be $5x^2$, that is the intended match.)

Answer:

$2x^3 + 5x^2 - x - 6$
(If selecting from the provided options, the closest intended answer is: $2x^3 + 6x^2 - x - 6$, assuming a typo in the coefficient of $x^2$)