The expression you provided is:

\[ 64y^6 - 112y^3z^7 + 49z^{14} \]

This expression appears to be a quadratic trinomial in terms of \( y^3 \) and \( z^7 \), which can be factored similarly to how you would factor a quadratic expression. Let's factor it step by step.

### Step 1: Recognize the quadratic form
The expression can be rewritten as:
\[ (8y^3)^2 - 2 \times 8y^3 \times 7z^7 + (7z^7)^2 \]

This fits the pattern of a perfect square trinomial:
\[ a^2 - 2ab + b^2 = (a - b)^2 \]

### Step 2: Identify \( a \) and \( b \)
In this case:
- \( a = 8y^3 \)
- \( b = 7z^7 \)

### Step 3: Apply the perfect square trinomial identity
Using the identity:
\[ (a - b)^2 = (8y^3 - 7z^7)^2 \]

So, the factored form of the expression is:
\[ (8y^3 - 7z^7)^2 \]

### Final Answer
\[ 64y^6 - 112y^3z^7 + 49z^{14} = (8y^3 - 7z^7)^2 \]

This is the factored form of the expression.

---

Would you like any details or have any questions?

Here are 8 related questions you might find interesting:
1. How do you identify a perfect square trinomial?
2. What other forms can quadratic expressions take?
3. Can you factor expressions that aren't perfect squares?
4. How does the distributive property relate to factoring?
5. What happens if the middle term was positive instead of negative?
6. How would you factor an expression with more variables?
7. Can you factor a cubic expression in a similar way?
8. What are common mistakes when factoring trinomials?

**Tip:** Always look for patterns like perfect squares or differences of squares when factoring complex expressions!

Learn how to factor the expression 64y^6 - 112y^3z^7 + 49z^14 using the perfect square trinomial identity. This problem involves factoring quadratic expressions with multiple variables and fits the pattern of a perfect square trinomial. Suitable for high school students studying algebra and factoring quadratic expressions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation