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c. Fill in the blanks.
1. The representation of an expression as the product of its factors is called ............... .

2
2. Factorised form of 4m – 12m + 9 is ............... .
2
2
3. Area of a rectangular plot with sides 5p and 6q is ............... .
4. The factors of ............... are (x + 5) and (3x + 7).
7x + 21
5. On simplification, = ............... .
7
D. State whether the following statements are true (t) or False (F).
1. The value of (a + 1)(a – 1)(a + 1) is a – 1.
4
2
2
2. y + (a + b)y + ab = (a + b)(y + ab).
2 2
2
2 2
3. Common factor of 12pq , 144p q and 1728p q is 12p q .
2
2
4. Factorised form of u + 30u + 216 is (u + 18)(u + 12).
5. To factorise an algebraic expression of the form ax + bx + c, we split b into two parts whose sum =
2
c and product = ac.
E. Solve the following questions.
1. Factorise the following:

2
(a) –5a + 5ab – 5ca (b) 24(3x – 4y) – 18(4y – 3x)
2
2
2 2
2
2 2 2
2
2
2
2
(c) 63p q r²s – 9pq r s +15p qr s² – 60p q²rs² (d) 2ax + 4axy + 3bx + 2ay + 6bxy + 3by 2
2. Find the value of:
.
.
.
625 × 6 25 175 × 1 75 198 × 198 − 102 × 102
−
.
(a) (b)
.
45 96
3. Divide the following polynomials by factorisation:
2
3
2
3
(a) 44(x – 2x – 15x) by 11x(x – 5) (b) 51x (98x – 32) by 34x (7x + 4)
2
4. Find the value of:
2
(16q − 16r 2 ) 1 1
2
‘
(a) ‘p’ if p(q – r) = (b) 16y + ’ if 4y − = 7
(qr+ ) 16y 2 4y
5. Simplify: (0.6x + 0.5y) – (0.6x – 0.5y) 2
2
2
2
6. If x – y = 13 and x + y = 20, then find x – y .
7. The height of a multi-storey building is (5a + 70a – 160) m. If the height of each of the floor of the
2
building is (a – 2) m, how many floors does the building have?
2
8. The curved surface area of a cylinder is 2p(y – 7y + 12) and its radius is (y – 3). Find the height of
the cylinder. (CSA of cylinder = 2prh) CompetenCy Based question
9. The cost of a chocolate is `(x + y) and Asif bought (x + y) chocolates. Find the total amount paid by
him in terms of x and y. If x = 10 and y = 5, find the amount paid by Asif.
10. Find the length of the side of the given square if the area of the square is 676 square units and then
find the value of x. CompetenCy Based question
(4x + 6)
(4x + 6)
309