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Find the missing factor D that makes the equality true. {:[-15y^(4)=(D)(3y^(2))],[D=◻]:}

Find the missing factor D D that makes the equality true.\newline−15y4=(D)(3y2)D=□ \begin{array}{l} -15 y^{4}=(D)\left(3 y^{2}\right) \\ D=\square \end{array}

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Full solution

Q. Find the missing factor D D that makes the equality true.\newline−15y4=(D)(3y2)D=□ \begin{array}{l} -15 y^{4}=(D)\left(3 y^{2}\right) \\ D=\square \end{array}
  1. Identify Given Equation: Identify the given equation and what we need to find.\newlineWe are given the equation −15y4=D×3y2-15y^4 = D \times 3y^2 and we need to find the value of DD.
  2. Divide by 3y23y^2: Divide both sides of the equation by 3y23y^2 to solve for DD.D=−15y43y2D = \frac{-15y^4}{3y^2}
  3. Simplify Right Side: Simplify the right side of the equation by canceling out common factors.\newlineD=(−15/3)×(y4/y2)D = (-15 / 3) \times (y^4 / y^2)\newlineD=−5×y4−2D = -5 \times y^{4-2}\newlineD=−5×y2D = -5 \times y^2
  4. Check Result: Check the result to ensure there are no mathematical errors.\newline−15y4=(−5×y2)×3y2-15y^4 = (-5 \times y^2) \times 3y^2\newline−15y4=−5×3×y2×y2-15y^4 = -5 \times 3 \times y^2 \times y^2\newline−15y4=−15y4-15y^4 = -15y^4\newlineThe left side of the equation matches the right side, confirming that D=−5×y2D = -5 \times y^2 is correct.

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