https://file.aiquickdraw.com/mathbot/file/17260365117031ojyvgj4.jpg

Let's go through each of the problems in the image step by step. I will provide detailed solutions for the problems listed.

### Problem 1:
\[
\frac{2x}{3y^2} \cdot \frac{15y^3}{8x}
\]
Simplifying:

1. Multiply the numerators: \( 2x \cdot 15y^3 = 30xy^3 \).
2. Multiply the denominators: \( 3y^2 \cdot 8x = 24xy^2 \).

Now cancel out common factors:  
- \( x \) cancels with \( x \),  
- \( y^2 \) in the denominator cancels with part of \( y^3 \) in the numerator, leaving \( y \).

So the simplified form is:
\[
\frac{30y}{24} = \frac{5y}{4}
\]

### Problem 2:
\[
\frac{x}{(2y)^2} \cdot \frac{y^2}{x}
\]
Simplifying:

1. \((2y)^2 = 4y^2\), so the expression becomes:
   \[
   \frac{x}{4y^2} \cdot \frac{y^2}{x}
   \]
2. Cancel \( x \) and \( y^2 \) (as they appear in both the numerator and denominator):
   \[
   \frac{1}{4}
   \]

So the answer is:
\[
\frac{1}{4}
\]

### Problem 3:
\[
\frac{a^2 - b^2}{a^2} \cdot \frac{a}{3b - 3a}
\]
First, recognize that \( a^2 - b^2 \) is a difference of squares:
\[
a^2 - b^2 = (a - b)(a + b)
\]

Now the expression becomes:
\[
\frac{(a - b)(a + b)}{a^2} \cdot \frac{a}{3(b - a)}
\]

Notice that \( 3(b - a) = -3(a - b) \). Using this, the expression becomes:
\[
\frac{(a - b)(a + b)}{a^2} \cdot \frac{a}{-3(a - b)}
\]
Cancel out \( a - b \):
\[
\frac{a + b}{a^2} \cdot \frac{a}{-3}
\]
Now simplify:
\[
\frac{a(a + b)}{-3a^2} = \frac{a + b}{-3a}
\]

So the answer is:
\[
\frac{-(a + b)}{3a}
\]

### Problem 4:
\[
\frac{2m^2 - 50}{5m^2 - 80} \cdot \frac{4m + 16}{3m - 15}
\]
First, factor both numerators and denominators:

- \( 2m^2 - 50 = 2(m^2 - 25) = 2(m - 5)(m + 5) \),
- \( 5m^2 - 80 = 5(m^

Multiply and simplify the following algebraic fractions as shown in the image.

Solve and simplify these practice problems involving the multiplication of algebraic fractions. This set covers important algebraic concepts such as simplifying fractions, factoring, and applying the difference of squares theorem. Suitable for students in Grades 8-10.

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