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poizon [28]
3 years ago
12

Using the distributive property, Marta multiplied the binomial (2x + 3) by the trinomial (x2 + x – 2) and got the expression bel

ow.
(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
Mathematics
2 answers:
Crazy boy [7]3 years ago
5 0

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

densk [106]3 years ago
3 0

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.

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