# NCERT solutions for Exercise 9.2 Class 8 Maths Chapter 9 Algebraic Expressions And Identities

1.Find the product of the following pairs of monomials :
(i) 4, 7p

(ii) -4p, 7p

(iii) – 4p, 7pq

(iv) 4p3 , – 3p

(v) 4p, 0

(i)Multiplying the given expressions: $$4 x\times 7p = (4 \times 7) \times p = 28p$$

(ii) Multiplying the given expressions:$$– 4 p \times 7p = (- 4 \times 7) \times (p\times p)$$

$$= -28p^{(1 + 1)} = – 28p^2$$

(iii)Multiplying the given expressions: $$-4p\times 7pq = (- 4 \times 7) \times (p \times p \times q)$$

$$= -28 p^{(1+1)}q = – 28p^2q$$

(iv)Multiplying the given expressions: $$4p3 \times – 3p = (4 \times – 3) \times (p^3 \times p)$$

$$= – 12p^{(3+1)} = =-12p^4$$

(v) Multiplying the given expressions:$$4p \times 0 = (4 \times 0) \times p = 0 \times p = 0$$

2.Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively.
$$(p, q); (10m, 5n); (20x^2, 5y^2); (4x, 3x^2); (3mn, 4np)$$

(i) Given that: Length = p units and breadth = q units

Area of the rectangle = $$length \times breadth = p \times q = pq$$ sq units

(ii)Given that: Length = 10 m units, breadth = 5n units

∴Area of the rectangle =$$length \times breadth = 10 m \times 5 n = (10 \times 5) \times m \times n = 50 mn\;$$sq units

(iii) Given that: Length = 20x2 units, breadth = 5y2 units

∴Area of the rectangle = length × breadth = 20x2 × 5y2 = (20 × 5) × x2 × y2 = 100x2y2 sq units

(iv)Given that: Length = 4x units, breadth = 3x2 units

∴Area of the rectangle = $$length \times breadth = 4x \times 3x^2 = (4 \times 3) \times x \times x^2 = 12x^3\;$$ sq units

(v) Given that: Length = 3mn units, breadth = 4np units

∴Area of the rectangle = $$length \times breadth = 3mn \times 4np = (3 \times 4) \times mn \times np = 12mn^2p\;$$ sq units

3.Complete the table of products :

Completed table is as under :

5. Obtain the product of

(i) xy, yz, zx

(ii) a, -a2, a3

(iii) 2, 4y, 8y2, 16y3

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

(v) m, -mn, mnp

(i) Product=$$xy \times yz \times zx = x^2y^2z^2$$
(ii) Product=$$a \times (-a^2) \times a^3 = (-a)^6$$
(iii)Product=$$2 \times 4y \times 8y^2 \times 16y^3 = (2 \times 4 \times 8 \times 16) \times y \times y^2 \times y^3 = 1024y^6$$
(iv)Product=$$a \times 2b \times 3c \times 6abc = (1 \times 2 \times 3 \times6) \times a \times b \times c \times abc = 36 a^2b^2c^2$$
(v)Product=$$m \times (-mn) \times mnp = [1 \times (-1) \times 1 ]m \times mn \times mnp = -m^3n^2p$$