The image contains three algebraic expressions, and it asks to factor each expression. Let's analyze and solve each one.

(1) $2x^2 + 15xy - 8y^2$

We need to factor this trinomial expression. First, let's look for two numbers that multiply to give $2 \times (-8) = -16$ and add up to $15$. These two numbers are $16$ and $-1$.

Rewrite the middle term using these numbers: $2x^2 + 16xy - xy - 8y^2$

Now, group the terms: $(2x^2 + 16xy) - (xy + 8y^2)$

Factor each group: $2x(x + 8y) - y(x + 8y)$

Now factor out the common binomial factor $(x + 8y)$: $(2x - y)(x + 8y)$

So, the factored form of $2x^2 + 15xy - 8y^2$ is: $(2x - y)(x + 8y)$

(2) $a^3b + a^2b^2 + a^2bc$

In this expression, we can factor out the common term $a^2b$: $a^2b(a + b + c)$

So, the factored form of $a^3b + a^2b^2 + a^2bc$ is: $a^2b(a + b + c)$

(3) $9x^2 + 12xy + 4y^2$

This is a perfect square trinomial. It can be factored as: $(3x + 2y)^2$

Summary of the factored forms:

1. $2x^2 + 15xy - 8y^2 = (2x - y)(x + 8y)$
2. $a^3b + a^2b^2 + a^2bc = a^2b(a + b + c)$
3. $9x^2 + 12xy + 4y^2 = (3x + 2y)^2$

Would you like further explanation on any of these steps? Let me know if you have any questions!

Related Questions:

1. How do you factor a trinomial like $ax^2 + bx + c$?
2. What is the difference between factoring a perfect square and a general trinomial?
3. Can the method of grouping be applied to any type of polynomial?
4. How do you handle negative signs when factoring?
5. What is the role of the distributive property in factoring?

Tip: When factoring, always start by identifying and factoring out the greatest common factor (GCF) first, as it simplifies the process!