Answer :
To factor the common factor out of the expression [tex]\(15x^3y + 25x^3\)[/tex], follow these steps:
1. Identify the Common Factor:
Look for common factors in each term of the expression. The terms are [tex]\(15x^3y\)[/tex] and [tex]\(25x^3\)[/tex].
- Both terms have [tex]\(x^3\)[/tex] in common.
- The coefficients [tex]\(15\)[/tex] and [tex]\(25\)[/tex] have a greatest common factor (GCF) of [tex]\(5\)[/tex].
2. Factor out the Common Factor:
Use the common factors identified in both terms to factor the expression. The common factor is [tex]\(5x^3\)[/tex].
- For the first term [tex]\(15x^3y\)[/tex]:
[tex]\[
15x^3y = 5x^3 \cdot 3y
\][/tex]
- For the second term [tex]\(25x^3\)[/tex]:
[tex]\[
25x^3 = 5x^3 \cdot 5
\][/tex]
3. Rewrite the Expression:
Combine the factored terms:
[tex]\[
15x^3y + 25x^3 = 5x^3(3y + 5)
\][/tex]
So, the expression [tex]\(15x^3y + 25x^3\)[/tex] factors to [tex]\(5x^3(3y + 5)\)[/tex].
1. Identify the Common Factor:
Look for common factors in each term of the expression. The terms are [tex]\(15x^3y\)[/tex] and [tex]\(25x^3\)[/tex].
- Both terms have [tex]\(x^3\)[/tex] in common.
- The coefficients [tex]\(15\)[/tex] and [tex]\(25\)[/tex] have a greatest common factor (GCF) of [tex]\(5\)[/tex].
2. Factor out the Common Factor:
Use the common factors identified in both terms to factor the expression. The common factor is [tex]\(5x^3\)[/tex].
- For the first term [tex]\(15x^3y\)[/tex]:
[tex]\[
15x^3y = 5x^3 \cdot 3y
\][/tex]
- For the second term [tex]\(25x^3\)[/tex]:
[tex]\[
25x^3 = 5x^3 \cdot 5
\][/tex]
3. Rewrite the Expression:
Combine the factored terms:
[tex]\[
15x^3y + 25x^3 = 5x^3(3y + 5)
\][/tex]
So, the expression [tex]\(15x^3y + 25x^3\)[/tex] factors to [tex]\(5x^3(3y + 5)\)[/tex].
