In the expression $xy^2$, the values of both variables $x$ and $y$ are decreased by 20%. By this, the value of the expression is decreased by

### Concept & Formula The value of an algebraic expression depends on the product of its variables. When each variable undergoes a percentage change, the overall expression undergoes successive percentage changes. For an expression of the form $xy^2$, the final scaling factor is the product of the individual scaling factors of $x$, $y$, and $y$. ### Step-by-Step Solution * **Initial Value:** Let the original values of the variables be $x$ and $y$. The initial value of the expression is $V_1 = x y^2$. * **Applying the Decreases:** Both variables decrease by $20\%$. New value of $x = x - 0.20x = 0.8x$. New value of $y = y - 0.20y = 0.8y$. * **Calculating the New Value:** Substitute the new variable values into the original expression: $V_2 = (0.8x) \times (0.8y)^2$ $V_2 = 0.8x \times 0.64y^2$ $V_2 = 0.512 x y^2$. * **Determining Percentage Decrease:** The new value is $51.2\%$ of the original value. Decrease in value = Initial Value - New Value Decrease = $1 V_1 - 0.512 V_1 = 0.488 V_1$. Percentage Decrease = $0.488 \times 100 = 48.8\%$. ### Exam Strategy & Shortcut Use multiplier fractions directly. A $20\%$ decrease means multiplying by $\frac{4}{5}$ or $0.8$. The expression is $x \cdot y \cdot y$. Multiplier = $0.8 \times 0.8 \times 0.8 = 0.512$. The remaining value is $51.2\%$. Therefore, the decrease is $100\% - 51.2\% = 48.8\%$. This can be calculated mentally in seconds. ### Common Pitfall A very common mistake is finding the new value ($51.2\%$) and blindly selecting it as the answer (Option C). The question asks for the *decrease* in value, which is $100\% - 51.2\% = 48.8\%$. Always double-check what the question is asking for! ### Final Answer **Therefore, the correct answer is 48.8%.**