DAV Class 8 Maths Chapter 7 Value Based Questions
Algebraic Identities Value Based Questions
1. In the vacations Gautam purchased \( \color{magenta} (x^2 + 8x - 20)\) game CDs, while Sanyam purchased \(\color{magenta} (x + 4)^2\) game CDs.
(i) Who purchased more CDs and by how much?
Solution
\[ \begin{aligned} \text{Gautam} &= x^2+8x-20 \\[4pt] \text{Sanyam} &= (x+4)^2 \\[4pt] & \implies x^2+8x+16 \\[6pt] \text{Difference} &= (x^2+8x+16)-(x^2+8x-20) \\[4pt] &= \cancel{x^2} + \cancel{8x} + 16 - \cancel{x^2} - \cancel{8x} + 20 \\[4pt] &=16 + 20 \\[4pt] &= 36 \\[4pt] \end{aligned} \]
Answer \( \color{red} Sanyam \) purchased more CDs, by \( \color{red}{36} \)
(ii) Write any one advantage and one disadvantage of playing video games.
Answer
Advantage: Entertainment
Disadvantage: Obesity, distraction, waste of time, etc.
2. On the Earth Day, cubical flower pots (with plants) of base area \( \color{magenta}(x^2+6x+9)\) square units were placed on a rectangular lane of area \( \color{magenta}(x+3)(7x+21)\) square units.
(i) How many pots were placed?
Solution
\[ \begin{aligned} \text{Base area of flower pots} &= x^2+6x+9 \\[4pt] &= (x)^2 + 2(x)(3) + (3)^2 \\[4pt] & \implies (x+3)^2 \\[8pt] \text{Area of lane} &= (x+3)(7x+21) \\[4pt] &= (x+3) \ 7(x+3) \\[4pt] &= 7(x+3)(x+3) \\[4pt] &= 7(x+3)^2 \\[8pt] \color{green}\text{Number of pots} &= \color{green}\frac{\text{Area of lane}}{\text{Base area of 1 pot}} \\[8pt] &= \frac{7\cancel{(x+3)^2}}{\cancel{(x+3)^2}} \\[8pt] &= 7 \ pots \end{aligned} \]
Answer \(\color{red}{7}\) pots were placed
(ii) Write the importance of trees in our life.
Answer Oxygen, reduce air pollution, provide habitat and shade, conserve soil and water, and help keep the climate balanced.