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) 12x^{2}y

Answer:

12x^{2}y

= 3x × 4xy OR 4x × 3xy OR 3x^{2} × 4y OR x^{2} × 12y

(ii) 18ab^{2}

Answer:

18ab^{2}

= 6a × 3b^{2} OR 3a × 6b^{2} OR 9a × 2b^{2} OR 2a × 9b^{2}

(iii) 24c^{2}b

Answer:

24c^{2}b

= 6c^{2} × 4b OR 6b × 4c^{2} OR 8b × 3c^{2} OR 3b × 8c^{2}

Question 2.

Find the H.C.F. of the following monomials:

(i) 2a^{5} and 12a^{2}

Answer:

2a^{5} and 12a^{2}

2 a^{5} = 2 × a × a × a × a × a

12 a^{2} = 2 × 2 × 3 × a × a

Common factors are 2, a, a

∴ H.C.F. = 2 × a × a = 2a^{2}

(ii) 9x^{3}y and 18x^{2}y^{3}

Answer:

9x^{3}y and 18x^{2}y^{3}

9x^{3}y = 3 × 3 × x × x × x × y

18x^{2}y^{3} = 2 × 3 × 3 × x × x × y × y × y

Common factors are 3, 3, x, x, y,

∴ H.C.F. = 3 × 3 × x × x × y = 9x^{2}y

(iii) a^{2}b^{3} and a^{3}b^{2}

Answer:

a^{2}b^{3} and a^{3}b^{2}

a^{2}b^{3} = a × a × b × b × b

a^{3}b^{2} = a × a × a × b × b

Common factors are a, a, b, b

∴ H.C.F. = a × a × b × b = a^{2}b^{2}

(iv) 15a^{3}, – 45a^{2},150a

Answer:

15a^{3}, – 45a^{2},150a

15a^{3} = 3 × 5 × a × a × a

– 45 a^{2} = – 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) 2x^{3}y^{2}, 10x^{2}y^{3},14xy

Answer:

2x^{3}y^{2}, 10x^{2}y^{3},14xy

2x^{3}y^{2} = 2 × x × x × x × y × y

10x^{2}y^{3} = 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) x^{3}y^{2}, – 8y^{2}

Answer:

x^{3}y^{2}, – 8y^{2}

x^{3}y^{2} = x × x × x × y × y

8y^{2} = – 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 – 15y^{2}

Answer:

5y – 15y^{2} = 5 × y – 3 × 5 × y × y

H.C.F. = 5y.

5y – 15y^{2} = 5y (1 – 3y^{2})

(ii) 16m – 4m^{2}

Answer:

16 m – 4 m^{2} = 2 × 2 × 2 × 2 × m – 2 × 2 × m × m

H.C.F. = 2 × 2 × m = 4m

16m – 4m^{2} = 4m (4 – m)

(iii) 8x^{3}y^{2} + 8x^{3}

Answer:

8x^{3}y^{2} + 8x^{3} = 2 × 2 × 2 × x × x × x × y × y + 2 × 2 × 2 × x × x × x

H.C.F. = 2 × 2 × 2 × x × x × x = 8x^{3}

8 x^{3}y^{2} + 8x^{3} = 8x^{3} (y^{2} + 1)

(iv) 20x^{3} – 40x^{2} + 80x

Answer:

20x^{3} – 40x^{2} + 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

20x^{3} – 40x^{2} + 80x = 20x (x^{2} – 2x + 4)

(v) x^{4}y – 3x^{2}y^{2} – 6xy^{3}

Answer:

x^{4}y – 3x^{2}y^{2} – 6 xy^{3} = x × x × x × x × y – 3 × x × x × y × y – 2 × 3 × x × y × y × y

H.C.F. = xy

x^{4}y – 3 x^{2}y^{2} – 6 xy^{3} = xy (x^{3} – 3xy – 6y^{2})

(vi) 8x^{2}y^{2} – 16xy^{3} + 24xy

Answer:

8x^{2}y^{2} – 16xy^{3} + 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

8x^{2}y^{2} – 16xy^{3} + 24xy = 8xy (xy – 2y^{2} + 3)