What is the result when the algebraic fraction 4X²/Y is multiplied by Y²/8X?

What is the result when the algebraic fraction 4X²/Y is multiplied by Y²/8X?

• A. X²Y/2
• B. XY/2
• C. 4XY/8
• D. X/Y

Answer: (B)

To find the result of multiplying the algebraic fractions \( \frac{4X^2}{Y} \) and \( \frac{Y^2}{8X} \), we start by applying the rule for multiplying fractions, which is to multiply the numerators together and the denominators together. The numerator of the first fraction is \( 4X^2 \) and the numerator of the second fraction is \( Y^2 \). When we multiply these, we get: \[ 4X^2 \times Y^2 = 4X^2Y^2 \] Next, we look at the denominators. The denominator of the first fraction is \( Y \) and the denominator of the second fraction is \( 8X \). When we multiply these together, we have: \[ Y \times 8X = 8XY \] Now we can combine both results into a single fraction: \[ \frac{4X^2Y^2}{8XY} \] To simplify this fraction, we can factor out common terms. In the numerator, \( 4X^2Y^2 \) can be rewritten as \( 4X \cdot X \cdot

To find the result of multiplying the algebraic fractions ( \frac{4X^2}{Y} ) and ( \frac{Y^2}{8X} ), we start by applying the rule for multiplying fractions, which is to multiply the numerators together and the denominators together.

The numerator of the first fraction is ( 4X^2 ) and the numerator of the second fraction is ( Y^2 ). When we multiply these, we get:

[

4X^2 \times Y^2 = 4X^2Y^2

]

Next, we look at the denominators. The denominator of the first fraction is ( Y ) and the denominator of the second fraction is ( 8X ). When we multiply these together, we have:

[

Y \times 8X = 8XY

]

Now we can combine both results into a single fraction:

[

\frac{4X^2Y^2}{8XY}

]

To simplify this fraction, we can factor out common terms. In the numerator, ( 4X^2Y^2 ) can be rewritten as ( 4X \cdot X \cdot