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

**(i) 4, 7p**

**Solution:**

= 4 × 7 × p

= 28p

**(ii) – 4p, 7p**

**Solution:**

= (-4 × 7) × (p × p)

= -28p^{2}

**(iii) – 4p, 7pq**

**Solution:**

= (-4 × 7) (p × pq)

= -28p^{2} q

**(iv) 4p ^{3}, – 3p**

**Solution:**

= (4 × -3) (p^{3} × p)

= -12p^{4}

**(v) 4p, 0**

**Solution: **

4p × 0 = 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)**

**Solution:**

We know that the area of rectangle = Length x breadth.

(i) p × q = pq sq units

(ii)10m × 5n = 50mn sq units

(iii) 20x^{2} × 5y^{2} = 100x^{2} y^{2} sq units

(iv) 4x × 3×2 = 12×3 sq units

(v) 3mn × 4np = 12mn^{2} p sq units

**3. Complete the following table of products:**

**Solution:**

**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 of rectangle = length x breadth x height.

Now,

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

^{4}

=5a x 3a^{2} x 7a^{4}

= (5 × 3 × 7) (a × a^{2} × a^{4})

= 105a^{7}

**(ii) 2p, 4q, 8r**

= 2p x 4q x 8r

= (2 × 4 × 8) (p × q × r)

= 64pqr

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

= y × 2x^{2} y × 2xy^{2}

= (1 × 2 × 2) (x × x^{2} × x × y × y × y^{2} )

= 4x^{4} y^{4}

**(iv) a, 2b, 3c**

= a x 2b x 3c

= (1 × 2 × 3) (a × b × c)

= 6abc

**5. Obtain the product of**

**(i) xy, yz, zx**

**Solution:**

= xy × yz × zx

= x^{2} y^{2} z^{2}

**(ii) a, – a ^{2} , a^{3}**

**Solution:**

= a × – a^{2} × a^{3}

= – a^{6}

**(iii) 2, 4y, 8y ^{2} , 16y^{3}**

**Solution:**

= 2 × 4y × 8y^{2} × 16y^{3}

= 1024 y^{6}

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

**Solution:**

= a × 2b × 3c × 6abc

= 36a^{2} b^{2}c^{2}

**(v) m, – mn, mnp**

**Solution:**

= m × – mn × mnp

= –m^{3} n^{2} p

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