Factoring: Difference of Two Squares Worksheet | Algebra I PDF ... - Free Printable

Final Answer:
2ab(a² - 4b²) = 2ab(a - 2b)(a + 2b)

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Explanation:
Let’s break this down step by step.

We are given:
2a³b – 8ab³

Step 1: Look for a common factor in both terms.
Both terms have 2, a, and b.
So, we can factor out 2ab.

Take 2ab out:
→ 2ab(a² – 4b²)

Step 2: Now look at what’s inside the parentheses:
a² – 4b²

This is a “difference of two squares”!
That means it fits the pattern:
X² – Y² = (X – Y)(X + Y)

Here, X = a, and Y = 2b (because (2b)² = 4b²)

So:
a² – 4b² = (a – 2b)(a + 2b)

Step 3: Put it all together:
2ab × (a – 2b)(a + 2b)

✔ Final answer: 2ab(a – 2b)(a + 2b)