https://r2.erweima.ai/mathbot/image/17268519400799coycz4t.jpg

The expression in the image is:

\[
4a^2b^2c^4 + 8a^5b^3c^4
\]

### Factoring the expression:

1. **Look for common factors** in both terms:
   - Both terms have \( c^4 \) as a factor.
   - The first term has \( 4a^2b^2 \), and the second term has \( 8a^5b^3 \).
   - Factor out the greatest common factor from both terms:
     - The common factor of \( a^2 \) can be factored out (since \( a^2 \) is the lowest power between \( a^2 \) and \( a^5 \)).
     - The common factor of \( b^2 \) can also be factored out (since \( b^2 \) is the lowest power between \( b^2 \) and \( b^3 \)).
     - The number 4 is the greatest common factor of 4 and 8.

2. **Factor out the common terms**:
   \[
   4a^2b^2c^4(1 + 2a^3b)
   \]

So the factored form of the expression is:

\[
4a^2b^2c^4(1 + 2a^3b)
\]

Would you like further details or have any questions?

### Related questions:
1. How do you identify the greatest common factor in an expression?
2. Can all expressions be factored, and if not, why?
3. What are some applications of factoring in algebra?
4. How would you simplify an expression with variables raised to powers?
5. What are the steps to factoring polynomials with multiple variables?

### Tip:
When factoring expressions with multiple variables, always start by looking for the greatest common factor (GCF) across all terms before applying other factoring techniques.

Factor the expression: 4a^2b^2c^4 + 8a^5b^3c^4

Learn how to factor the polynomial expression 4a^2b^2c^4 + 8a^5b^3c^4 by extracting the greatest common factor. This problem introduces key algebraic concepts like factoring and the properties of exponents, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation