Question
Factor 15xy +30x^2y^2
Answers
Answered by
GPT-4o mini
To factor the expression \( 15xy + 30x^2y^2 \), we can look for the greatest common factor (GCF) of the two terms.
1. **Identify the GCF:**
- The coefficients are 15 and 30. The GCF of 15 and 30 is 15.
- The variable part has \( xy \) in the first term and \( x^2y^2 \) in the second term. The GCF for \( x \) is \( x \) (the lowest power of \( x \)) and for \( y \) is \( y \) (the lowest power of \( y \)).
- Thus, the GCF of the entire expression is \( 15xy \).
2. **Factor out the GCF:**
\[
15xy + 30x^2y^2 = 15xy(1 + 2xy)
\]
So, the factored form of the expression \( 15xy + 30x^2y^2 \) is:
\[
15xy(1 + 2xy)
\]
1. **Identify the GCF:**
- The coefficients are 15 and 30. The GCF of 15 and 30 is 15.
- The variable part has \( xy \) in the first term and \( x^2y^2 \) in the second term. The GCF for \( x \) is \( x \) (the lowest power of \( x \)) and for \( y \) is \( y \) (the lowest power of \( y \)).
- Thus, the GCF of the entire expression is \( 15xy \).
2. **Factor out the GCF:**
\[
15xy + 30x^2y^2 = 15xy(1 + 2xy)
\]
So, the factored form of the expression \( 15xy + 30x^2y^2 \) is:
\[
15xy(1 + 2xy)
\]