Question

Find the step-by-step process to factor the expression 48x^2y - 72xy^2

Answer 1

To factor the expression \( 48x^2y - 72xy^2 \), follow these steps:

1. **Identify the Greatest Common Factor (GCF)**:
- First, look for the coefficients: 48 and 72.
- The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
- The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
- The GCF of 48 and 72 is 24.

Next, look at the variables:
- The expression has \( x^2y \) and \( xy^2 \).
- The GCF of \( x^2 \) and \( x \) is \( x \).
- The GCF of \( y \) and \( y^2 \) is \( y \).
- Therefore, the overall GCF of the expression \( 48x^2y - 72xy^2 \) is \( 24xy \).

2. **Factor out the GCF**:
- Now that we have the GCF \( 24xy \), we can factor it out of each term in the expression.
- Rewrite the expression by dividing each term by the GCF:
\[
48x^2y \div 24xy = 2x \quad \text{and} \quad 72xy^2 \div 24xy = 3y
\]
- So when we factor out \( 24xy \), we get:
\[
48x^2y - 72xy^2 = 24xy(2x - 3y)
\]

3. **Write the final factored form**:
- Therefore, the expression factored completely is:
\[
24xy(2x - 3y)
\]

In conclusion, the factored form of \( 48x^2y - 72xy^2 \) is \(\boxed{24xy(2x - 3y)}\).