Questions: Which of the following are binomials? Select all correct answers. Select all that apply: 2x^2y^2z^2+2xyz 3xy+3x 3x^2yz^2+2x^2

Transcript text: Which of the following are binomials? Select all correct answers. Select all that apply: $2 x^{2} y^{2} z^{2}+2 x y z$ $3 x y+3 x$ $3 x^{2} y z^{2}+2 x^{2}$

Solution

Solution Steps

Step 1: Understanding Binomials

A binomial is a polynomial with exactly two terms. Each term is a product of constants and variables raised to non-negative integer powers.

Step 2: Analyzing Each Option

Let's analyze each given option to determine if it is a binomial.

$2x^{2}y^{2}z^{2} + 2x^{2} + 2xyz$
- This expression has three terms: $2x^{2}y^{2}z^{2}$, $2x^{2}$, and $2xyz$.
- It is not a binomial.
$2x^{2}y^{2}z^{2} + 2xyz$
- This expression has two terms: $2x^{2}y^{2}z^{2}$ and $2xyz$.
- It is a binomial.
$3x^{2}yz$
- This expression has only one term.
- It is not a binomial.
$3xy + 3x$
- This expression has two terms: $3xy$ and $3x$.
- It is a binomial.
$3x^{2}yz^{2} + 2x^{2}$
- This expression has two terms: $3x^{2}yz^{2}$ and $2x^{2}$.
- It is a binomial.
$3x^{2} + 3xy + 2x$
- This expression has three terms: $3x^{2}$, $3xy$, and $2x$.
- It is not a binomial.