Let's factor the given expression [tex]\(8x^2y + 16xy\)[/tex] step by step.
1. Identify the common factors:
First, look at both terms in the expression [tex]\(8x^2y + 16xy\)[/tex].
- The first term is [tex]\(8x^2y\)[/tex].
- The second term is [tex]\(16xy\)[/tex].
2. Factor out the greatest common factor (GCF):
- Identify the common numerical factor: Both 8 and 16 have a common numerical factor of 8.
- Identify the common variable factors: Both terms have the variable factors [tex]\(x\)[/tex] and [tex]\(y\)[/tex]. The smallest power of [tex]\(x\)[/tex] present in both terms is [tex]\(x^1\)[/tex] (since [tex]\(x^1\)[/tex] is implied in [tex]\(16xy\)[/tex]), and the smallest power of [tex]\(y\)[/tex] present in both terms is [tex]\(y\)[/tex].
3. Combine these common factors:
The greatest common factor is [tex]\(8xy\)[/tex].
4. Factor out the GCF:
We write the original expression as a product of the GCF and another expression:
[tex]\[
8x^2y + 16xy = 8xy \left(\frac{8x^2y}{8xy} + \frac{16xy}{8xy}\right)
\][/tex]
5. Simplify the expression inside the parentheses:
- Simplify [tex]\(\frac{8x^2y}{8xy}\)[/tex]:
[tex]\[
\frac{8x^2y}{8xy} = \frac{8 \cdot x^2 \cdot y}{8 \cdot x \cdot y} = x
\][/tex]
- Simplify [tex]\(\frac{16xy}{8xy}\)[/tex]:
[tex]\[
\frac{16xy}{8xy} = \frac{16}{8} = 2
\][/tex]
6. Write the factored form:
So the expression inside the parentheses simplifies to:
[tex]\[
8xy(x + 2)
\][/tex]
Therefore, the factored form of the given expression [tex]\(8x^2y + 16xy\)[/tex] is:
[tex]\[
8xy(x + 2)
\][/tex]
