Question

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 1

Answer:

option C is correct

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

Step-by-step explanation:

The distributive property states that:

$a \cdot (x+y+z) = a \cdot x +a \cdot y+a \cdot z$

Given that:

Marta multiplied the binomial (2x + 3) by the trinomial $(x^2 + x -2)$

i.e,

$(2x+3)(x^2+x-2)$

Distribute first term of the binomial to the trinomial expression and second term of the binomial to the trinomial expression.

$2x(x^2+x-2)+3(x^2+x-2)$

Apply the distributive property:

$(2x)(x^2)+(2x)(x)-(2x)(2)+(3)(x^2)+(3)(x)-(3)(2)$

Simplify:

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

Combine like terms:

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

Therefore, the simplified product of the given expression is: $2x^3+5x^2-x-6$

Answer 2

Marta got the expression

$2x\cdot x^2 + 2x\cdot x + 2x\cdot (-2) + 3\cdot x^2 + 3\cdot x + 3\cdot (-2).$

First, note that

$2x\cdot x^2=2x^3,\\2x\cdot x=2x^2,\\2x\cdot (-2)=-4x,\\3\cdot x^2=3x^2,\\ 3\cdot x=3x,\\3\cdot (-2)=-6.$

Then add terms with the same degree:

$2x^2+3x^2=5x^2,\\-4x+3x=-x.$

At last,

$(2x+3)(x^2 + x - 2)=2x^3+5x^2-x-6.$

Answer: correct choice is C.