Question:

Simplify: \[ \frac{x^3 \times 2x^4 \times 5y + 4y^2 + 3y^2}{y} \]

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When simplifying expressions with exponents, first multiply or divide the variables with like bases and then combine like terms.
Updated On: Sep 30, 2025
  • \( 10x^7 + 7y \)
  • \( 15x^6 + 3y^2 \)
  • \( 5x^7 + 7y \)
  • \( 3x^7 + y \)
  • \( 15x^6 + y^2 \)
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The Correct Option is A

Solution and Explanation

Step 1: Simplify the numerator.
The expression in the numerator is: \[ x^3 \times 2x^4 \times 5y + 4y^2 + 3y^2. \]

Step 2: Combine like terms. First, simplify \( x^3 \times 2x^4 = 2x^7 \), so the first term becomes: \[ 2x^7 \times 5y = 10x^7y. \]
Now, simplify the rest: \[ 4y^2 + 3y^2 = 7y^2. \]

Step 3: Divide by \( y \). Now divide the entire expression by \( y \): \[ \frac{10x^7y + 7y^2}{y} = 10x^7 + 7y. \]
Thus, the simplified expression is \( 10x^7 + 7y \).
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