To simplify the expression [tex]\(25x^2y^3 + 55xy^3\)[/tex], let's follow these steps:
1. Identify Common Factors:
- First, observe that both terms in the expression [tex]\(25x^2y^3\)[/tex] and [tex]\(55xy^3\)[/tex] have a common factor. In this case, both terms contain [tex]\(y^3\)[/tex].
2. Factor Out [tex]\(y^3\)[/tex]:
- You can factor the common term [tex]\(y^3\)[/tex] out of each term in the expression:
[tex]\[
25x^2y^3 + 55xy^3 = y^3(25x^2 + 55x)
\][/tex]
3. Factor Out Common Factors Further:
- Now, inside the parentheses, [tex]\(25x^2 + 55x\)[/tex] still has a common factor, which is [tex]\(x\)[/tex]. So, you can factor [tex]\(x\)[/tex] out from each term:
[tex]\[
y^3(25x^2 + 55x) = y^3 \cdot x (25x + 55)
\][/tex]
4. Write the Final Simplified Expression:
- Now, combining everything together, the expression is simplified to:
[tex]\[
y^3 \cdot x \cdot (25x + 55)
\][/tex]
So, the simplified form of the given expression [tex]\(25x^2y^3 + 55xy^3\)[/tex] is:
[tex]\[
y^3 \cdot x \cdot (25x + 55)
\][/tex]
