Understanding Monomials
Monomials are algebraic expressions that consist of a single term. They can be represented by a coefficient and variables raised to non-negative integer powers. The goal is to find two monomials that, when multiplied together, yield the expression 5xyz.
Identifying Coefficients and Variables
To find two monomials with positive integer coefficients, we start by breaking down the product:
- The coefficient in the product 5xyz is 5.
- The variables involved are x, y, and z.
Finding the Monomials
We seek two monomials whose product equals 5xyz. Here’s how we can approach this:
- Monomial 1: 5x
- Monomial 2: yz
When we multiply these two monomials, we get:
- (5x) * (yz) = 5xyz
This satisfies our original expression.
Alternative Monomials
Another pair of monomials could also work. Let’s explore:
- Monomial 1: 1x (which is simply x)
- Monomial 2: 5yz
Again, when we multiply these two:
- (1x) * (5yz) = 5xyz
This pair also meets the requirement.
Conclusion
In summary, two sets of monomials that can give us the product of 5xyz are:
- 5x and yz
- x and 5yz
Both pairs have positive integer coefficients and satisfy the condition.