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
Answer:
12x²y
= 3x × 4xy OR 4x × 3xy OR 3x² × 4y OR x² × 12y

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

(iii) 24c²b
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
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
Answer:
5y – 15y² = 5 × y – 3 × 5 × y × y
H.C.F. = 5y.
5y – 15y² = 5y (1 – 3y²)

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

(iii) 8x³y² + 8x³
Answer:
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
Answer:
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
Answer:
x⁴y – 3x²y² – 6 xy³ = x × x × x × x × y – 3 × x × x × y × y – 2 × 3 × x × y × y × y
H.C.F. = xy
x⁴y – 3 x²y² – 6 xy³ = xy (x³ – 3xy – 6y²)

(vi) 8x²y² – 16xy³ + 24xy
Answer:
8x²y² – 16xy³ + 24xy = 2 × 2 × 2 × x × x × y × y – 2 × 2 × 2 × 2 × x × y × y × y + 2 × 2 × 2 × 3 × x × y
H.C.F. = = 2 × 2 × 2 × x × y = 8 xy
8x²y² – 16xy³ + 24xy = 8xy (xy – 2y² + 3)