Question

Organize the following expressions from greatest to least by number of terms:

I. x + 2xyz
II. 3x + y + z
III. 2x2y + x2 − 3x + 4
IV. 9x2yz

Answer 1

the order is III, II, I, IV

Answer 2

`2x^2y + x^2 - 3x + 4~ (4)>3x + y + z ~(3)>x + 2xyz ~(2)>9x^2yz~ (1)`

Explanation:

We are given expressions in the question.

Term in an expression:

• Each expression constitute terms.
• A term can be a number, a variable, or a constant multiplied by a variable or variables.
• Each term in an algebraic expression is separated by a + sign or - sign.

We need to find the number of terms in each expression:

1)

`x + 2xyz\\\text{Number of terms}= 2`

2)

`3x + y + z\\\text{Number of terms}= 3`

3)

`2x^2y + x^2 - 3x + 4\\\text{Number of terms} = 4`

4)

`9x^2yz\\\text{Number of terms} = 1`

Arranged from greatest to least by number of terms:

`2x^2y + x^2 - 3x + 4~ (4)>3x + y + z ~(3)>x + 2xyz ~(2)>9x^2yz~ (1)`