**
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
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(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.
\((p, q); (10m, 5n); (20x^2, 5y^2); (4x, 3x^2); (3mn, 4np)\)
**

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(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

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
**

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(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=\( m \times (-mn) \times mnp = [1 \times (-1) \times 1 ]m \times mn \times mnp = -m^3n^2p\)