Is it possible to factor the expression 14x^9(y + 10) + 4(y + 10). If so, factor it.

Yes, it is possible to factor the expression \( 14x^9(y + 10) + 4(y + 10) \).

Let's go through the steps:

### Step 1: Identify the common factor
Both terms in the expression have a common factor of \( (y + 10) \).

### Step 2: Factor out the common factor
Factor out \( (y + 10) \) from each term:

\[
14x^9(y + 10) + 4(y + 10) = (y + 10)(14x^9 + 4)
\]

### Step 3: Simplify the remaining expression
Now, look at the expression inside the parentheses:

\[
14x^9 + 4
\]

You can factor out a common factor of 2:

\[
14x^9 + 4 = 2(7x^9 + 2)
\]

### Step 4: Substitute back
Substitute this back into the expression:

\[
(y + 10)(14x^9 + 4) = (y + 10) \times 2(7x^9 + 2)
\]

### Final Factored Form
The fully factored form of the expression is:

\[
2(y + 10)(7x^9 + 2)
\]

Would you like any further details or have any questions?

Here are some related questions you might find helpful:
1. How do you factor expressions with multiple terms?
2. What is the significance of identifying the greatest common factor (GCF) in factoring?
3. Can you explain how to factor trinomials?
4. What are some special cases in factoring, like the difference of squares?
5. How do you factor cubic polynomials?

**Tip:** Always look for the greatest common factor (GCF) first when factoring any algebraic expression. This simplifies the process and reduces the complexity of further steps.

Discover how to factor the expression 14x^9(y + 10) + 4(y + 10) with a detailed step-by-step solution. This problem covers key algebraic concepts, including factoring polynomials and simplifying expressions. Suitable for students in Grades 9-12.

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