Question

Find the GCF of the three terms below

20xy^2+10xy^3+15x^3y^2

and rewrite the expression by factoring out the GCF

Answer 1

`GCF=5x {y}^(2) </p><p>`

`5x {y}^(2) (4+ 2y + 3{x}^2 )`

Step-by-step explanation

The given expression is

`20x {y}^(2) + 10x {y}^(3) + 15 {x}^(3) {y}^(2)`

This can be rewritten as:

`{2}^(2) * 5x {y}^(2) + 2 * 5x {y}^(3) + 3 * 5{x}^(3) {y}^(2)`

The greatest common factor is the product of the least powers of the factors common to all the terms;

`GCF=5x {y}^(2) </p><p>`

We factor to obtain;

`5x {y}^(2) (4+ 2y + 3{x}^2 )`