Question

Arrange the following expressions from the greatest to the least number of terms:

1. x+2xyz
2. 9x²yz
3. 18x²+5ab-6y
4. 4x³+3x²-x-4

Answer 1

To arrange the given algebraic expressions by the number of terms from greatest to least, count the terms separated by plus or minus signs. The expressions ordered from greatest to least number of terms are 4x³+3x²-x-4, 18x²+5ab-6y, x+2xyz, and 9x²yz.

Step-by-step explanation:

The question involves arranging algebraic expressions based on number of terms they have from greatest to least. To count the terms in an algebraic expression, we look for pieces of the expression that are separated by a plus (+) or minus (-) sign. Now, let's count the terms:

1. x+2xyz has 2 terms.
2. 9x²yz has 1 term.
3. 18x²+5ab-6y has 3 terms.
4. 4x³+3x²-x-4 has 4 terms.

Therefore, the expressions arranged from greatest to least number of terms are:

1. 4x³+3x²-x-4 (4 terms)
2. 18x²+5ab-6y (3 terms)
3. x+2xyz (2 terms)
4. 9x²yz (1 term)