Question

Find the greatest common factor of 30x³y - 45x²y² and 135xy³.

a) 15xy
b) 30xy²
c) 45xy³
d) 60xy⁴

Answer 1

The greatest common factor of the expressions 30x³y - 45x²y² and 135xy³ is a)15xy.

Step-by-step explanation:

To find the greatest common factor (GCF) of the expressions 30x³y - 45x²y² and 135xy³, we need to factor out the common terms from both expressions.

First, we list the factors of the numerical coefficients:

• The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.
• The factors of 45 are 1, 3, 5, 9, 15, 45.
• The factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135.

Next, we find the common numerical factor of 30, 45, and 135, which is 15.

Now, we look at the variable part. The smallest power of x that appears in the terms is x, and the smallest power of y is y.

Combining the numerical coefficient with the variable part, we get that the GCF is 15xy.

Thus, the greatest common factor of 30x³y - 45x²y² and 135xy³ is 15xy, which corresponds to option (a).