Question 1. Find the product of the following pairs of monomials.
Monomial: Expression containing only one term
(i) 4, 7p
Ans:
(4) * (7p) = 28p
(ii) -4p, 7p
Ans:
(-4p) * (7p) = -28p^{2}
Explanation: When a negative number is multiplied to a positive number the product becomes negative.
(iii) -4p, 7pq
Ans:
(-4p) * (7pq) = -28p^{2}q
(iv) 4p^{3}, -3p
Ans:
(4p^{3}) * (-3p) = -12p^{4}
(v) 4p, 0
Ans:
(4p) * (0) = 0
Explanation: Any number when multiplied to zero (0) gives zero.
Question 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)
Note: Area of rectangle is the product of length and breadth [length * breadth]
Ans:
For (p,q):
p * q = pq
For (10m, 5n):
10m * 5n = 50mn
For (20x^{2},5y^{2}):
20x^{2 }* 5y^{2} = 100x^{2}y^{2}
For (4x,3x^{2}):
4x * 3x^{2} = 12x^{3}
For (3mn, 4np):
3mn * 4np = 12mn^{2}p
Question 3. Complete the table of products.
Ans:
First monomial Second monomial |
2x | -5y | 3x^{2 } | -4xy | 7x^{2}y | -9x^{2}y^{2} |
2x | 4x^{2} | -10xy | 6x^{3} | -8x^{2}y | 14x^{3}y | -18x^{3}y^{2} |
-5y | -10xy | 25y^{2} | -15x^{2}y | 20xy^{2} | -35x^{2}y^{2} | 45x^{2}y^{3} |
3x^{2} | 6x^{3} | -15x^{2}y | 9x^{4} | -12x^{3}y | 21x^{4}y | -27x^{4}y^{2} |
-4xy | -8x^{2}y | 20xy^{2} | -12x^{3}y | 16x^{2}y^{2} | -28x^{3}y^{2} | 36x^{3}y^{3} |
7x^{2}y | 14x^{3}y | -35x^{2}y^{2} | 21x^{4}y | -28x^{3}y^{2} | 49x^{4}y^{2} | -63x^{4}y^{3} |
-9x^{2}y^{2} | -18x^{3}y^{2} | 45x^{2}y^{3} | -27x^{4}y^{2} | 36x^{3}y^{3} | 63x^{4}y^{3} | 81x^{4}y^{4} |
Question 4. Obtain the volume of rectangular boxes with the following length, breadth, and height respectively.
Note: The volume of the rectangle is the product of length, breadth, height [length * breadth * height]
(i) 5a, 3a^{2}, 7a^{4}
Ans:
5a * 3a^{2} * 7a^{4 }= 105a^{7}
(ii) 2p , 4q , 8r
Ans:
2p * 4q * 8r = 64pqr
(iii) xy, 2x^{2}y, 2xy^{2}
Ans:
xy * 2x^{2}y * 2xy^{2 }= 4x^{4}y^{4}
(iv) a, 2b, 3c
Ans: a * 2b * 3c = 6abc
Question 5. Obtain the product of
(i) xy, yz, zx
Ans:
xy * yz * zx = x^{2}y^{2}z^{2}
(ii) a, -a^{2}, a^{3}
Ans:
a * -a^{2 }* a^{3} = -a^{6}
(iii) 2, 4y, 8y^{2}, 16y^{3}
Ans:
2 * 4y * 8y^{2 }* 16y^{3} = 1024y^{6}
(iv) a, 2b, 3c, 6abc
Ans:
a * 2b * 3c * 6abc = 36a^{2}b^{2}c^{2}
(v) m, -mn, mnp
Ans:
m * -mn * mnp = -m^{3}n^{2}p