**NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.2 – Algebraic Expressions & Identities**

**Q.1 Find the product of the following pairs of monomials. **

**(i) 4, 7p
(ii) − 4p, 7p
(iii) − 4p, 7pq
(iv) 4p**

^{3}, − 3p (v) 4p, 0

**Solution: **

The product of pair of monomials:

**(i)** **(ii)** **(iii) ****(iv) ****(v) **

** **

**Q.2 Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively.**

(p,q); (10m, 5n); (20x², 5y²); (4x, 3x²); (3mn, 4np)

**Solution:**

We know that, Area of rectangle = length × breadth

Area of rectangle with length p and breadth q

= p × q = pq

Area of rectangle with length 10m and breadth 5n

= 10m × 5n = 10 × 5 × m × n = 50 mn

Area of rectangle with length 20x^{2} and breadth 5y^{2}

= 20x^{2} × 5y^{2} = 20 × 5 × x^{2} × y^{2} = 100 x^{2}y^{2}

Area of rectangle with length 4x and breadth 3x^{2}

= 4x × 3x^{2} = 4 × 3 × x × x^{2} = 12x^{3}

Area of rectangle with length 3mn and breadth 4np

= 3mn × 4np = 3 × 4 × m × n × n × p = 12mn^{2}p

** **

**Q.3 Complete the table of products.**

**Solution:**

**Q.4 Obtain the volume of rectangular boxes with the following length, breadth and height respectively**

**(i) 5a, 3a ^{2}, 7a^{4}**

(ii) 2p, 4q, 8r

(iii) xy, 2x^{2}y, 2xy^{2}

(iv) a, 2b, 3c

**Solution:**

We know that, Volume = Length × Breadth × Height

**(i)** Volume of rectangular box with length 5a, breadth 3a^{2} and height 7a^{4}

= 5a × 3a^{2} × 7a^{4} = 5 × 3 × 7 × a × a^{2} × a^{4} = 105 a^{7}

**(ii)** Volume of rectangular box with length 2p, breadth 4q and height 8r

= 2p × 4q × 8r = 2 × 4 × 8 × p × q × r = 64pqr

**(iii)** Volume of rectangular box with length xy, breadth 2x^{2}y and height 2xy^{2}

= xy × 2x^{2}y × 2xy^{2} = 2 × 2 × xy × x^{2}y × xy^{2} = 4x^{4}y^{4}

**(iv)** Volume of rectangular box with length a, breadth 2b and height 3c

= a × 2b × 3c = 2 × 3 × a × b × c = 6abc

**Q.5 Obtain the product of **

**(i) xy, yz, zx
(ii) a, − a ^{2}, a^{3}**

**(iii) 2, 4y, 8y**

(iv) a, 2b, 3c, 6abc

^{2}, 16y^{3}(iv) a, 2b, 3c, 6abc

**(v) m, − mn, mnp**

**Solution:**

**(i)** **(ii)** **(iii) ****(iv) ****(v) **

**NCERT Solutions For Class 8 Maths Chapter 9 Exercise 9.2 – Algebraic Expressions & Identities**

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