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C. Answer the following:

1. What should be added to 4c(–a + b + c) to obtain 3a(a + b + c) – 2b(a – b + c)?
2. The figure shows the dimensions of a wall with a window and a door 7x + 2
of a room. Write an algebraic expression for the area of the wall to be Door 2x

painted. CompetenCy Based Question x
7x
3. The cost of a pen is ₹(x + y) and Samarth bought (x + y), pens. Find the 5x Window
total amount paid by him in terms of x and y. Also, find the amount
paid by him if x = 8 and y = 4. x

2
4. What will be the area of the rectangle with dimensions (pq + 3q ) and (4p + 2pq) if p = 5 units and
2
q = 10 units?
 3  2
y
5. Expand the algebraic expression 4x + 2   using the identity, and evaluate the expression for


x = –1 and y = 2.
2
2
2
6. Verify that (11pq + 4q) – (11pq – 4q) = 176pq .
1 1
2
7. Find the value of 25p + if 5p − = 10 .
25p 2 5 p
2
2
8. If (a + b) = 36 and a + b = 256, then find the value of ab.
3
2
9. Divide 2x + 5x – 7x – 10 by (x + 1) using a long division method.
2
2
10. If s + t = 13 and st = 6, then find the value of each of the following expressions:
(a) s + t (b) s – t (c) s + t 4
4
2
11. The perimeter of a triangle is 27x – 20x + 11. If two of its sides are 5x + 8x – 3 and 8x – 3x + 12,
2
2
find its third side.
2
2
12. Maninder owns a rectangular agricultural land A having length 4x + x y
2
2
– 2xy and perimeter 8x + 2x y – 2xy – 4y . Later, he purchased another
2
agricultural land B adjacent to land A and combined the two lands into one.
2
The length of his agriculture land now increased by x + xy, while the Agriculture land A Agriculture land B Case study
breadth remains the same.
Based on the above information answer the following questions:
(a) Find the breadth of the agricultural land A. (b) Find the length of the combined land.
(c) Find the perimeter of the combined land. (d) Find the area of the agricultural land B.
www
MAths connect
We need protein in our daily diet to assist our body in repairing
cells and creating new ones. It is crucial in growth and development, Foods (per unit = 100g) Protein
particularly for children, teenagers, and pregnant women. Observe Milk 3.4 g
the given table: Egg 13 g
Write an algebraic expression for the amount of protein intake for Lentils 9 g
the following: Cottage Cheese 12.4 g
(a) x unit of milk and y unit of chicken breast. Chicken Breast 31 g
(b) 2x units of eggs and 1 unit of lentils.

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