# DAV Class 7 Maths Chapter 6 Worksheet 5 Solutions

The DAV Class 7 Maths Solutions and DAV Class 7 Maths Chapter 6 Worksheet 5 Solutions of Algebraic Expressions offer comprehensive answers to textbook questions.

## DAV Class 7 Maths Ch 6 WS 5 Solutions

Question 1.
Express the following as a product of its any two factors (in four different ways):
(i) 12x2y
12x2y
= 3x × 4xy OR 4x × 3xy OR 3x2 × 4y OR x2 × 12y

(ii) 18ab2
18ab2
= 6a × 3b2 OR 3a × 6b2 OR 9a × 2b2 OR 2a × 9b2

(iii) 24c2b
24c2b
= 6c2 × 4b OR 6b × 4c2 OR 8b × 3c2 OR 3b × 8c2

Question 2.
Find the H.C.F. of the following monomials:
(i) 2a5 and 12a2
2a5 and 12a2
2 a5 = 2 × a × a × a × a × a
12 a2 = 2 × 2 × 3 × a × a
Common factors are 2, a, a
∴ H.C.F. = 2 × a × a = 2a2

(ii) 9x3y and 18x2y3
9x3y and 18x2y3
9x3y = 3 × 3 × x × x × x × y
18x2y3 = 2 × 3 × 3 × x × x × y × y × y
Common factors are 3, 3, x, x, y,
∴ H.C.F. = 3 × 3 × x × x × y = 9x2y

(iii) a2b3 and a3b2
a2b3 and a3b2
a2b3 = a × a × b × b × b
a3b2 = a × a × a × b × b
Common factors are a, a, b, b
∴ H.C.F. = a × a × b × b = a2b2

(iv) 15a3, – 45a2,150a
15a3, – 45a2,150a
15a3 = 3 × 5 × a × a × a
– 45 a2 = – 3 × 3 × 5 × a × a
150 a = 2 × 3 × 5 × 5 × a
Common factors are 3, 5, a,
∴ H.C.F. = 3 × 5 × a = 15a

(v) 2x3y2, 10x2y3,14xy
2x3y2, 10x2y3,14xy
2x3y2 = 2 × x × x × x × y × y
10x2y3 = 2 × 5 × x × x × y × y × y
14 xy = 2 × 7 × x × y
Common factors are 2, x, y
H.C.F. = 2 × x × y = 2xy

(vi) x3y2, – 8y2
x3y2, – 8y2
x3y2 = x × x × x × y × y
8y2 = – 2 × 2 × 2 × y × y
Common factor is y
H.C.F. is y.

Question 3.
Find the H.C.F. of the terms and factorize:
(i) 5y – 15y2
5y – 15y2 = 5 × y – 3 × 5 × y × y
H.C.F. = 5y.
5y – 15y2 = 5y (1 – 3y2)

(ii) 16m – 4m2
16 m – 4 m2 = 2 × 2 × 2 × 2 × m2 × 2 × m × m
H.C.F. = 2 × 2 × m = 4m
16m – 4m2 = 4m (4 – m)

(iii) 8x3y2 + 8x3
8x3y2 + 8x3 = 2 × 2 × 2 × x × x × x × y × y + 2 × 2 × 2 × x × x × x
H.C.F. = 2 × 2 × 2 × x × x × x = 8x3
8 x3y2 + 8x3 = 8x3 (y2 + 1)

(iv) 20x3 – 40x2 + 80x
20x3 – 40x2 + 80x = 2 × 2 × 5 × x × x × x – 2 × 2 × 2 × 5 × x × x + 2 × 2 × 2 × 2 × 5 × x
H.C.F. = 2 × 2 × 5 × x = 20x
20x3 – 40x2 + 80x = 20x (x2 – 2x + 4)

(v) x4y – 3x2y2 – 6xy3