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Find the product of the following pairs of monomials.
(i) 4, 7p (ii) − 4p, 7p (iii) − 4p, 7pq
(iv) 4p3, − 3p (v) 4p, 0
The product will be as follows.
(i) 4 × 7p = 4 × 7 × p = 28p
(ii) − 4p × 7p = − 4 × p × 7 × p = (− 4 × 7) × (p × p) = − 28 p2
(iii) − 4p × 7pq = − 4 × p × 7 × p × q = (− 4 × 7) × (p × p × q) = − 28p2q
(iv) 4p3 × − 3p = 4 × (− 3) × p × p × p × p = − 12 p4
(v) 4p × 0 = 4 × p × 0 = 0
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)
We know that,
Area of rectangle = Length × Breadth
Area of 1st rectangle = p × q = pq
Area of 2nd rectangle = 10m × 5n = 10 × 5 × m × n = 50 mn
Area of 3rd rectangle = 20x2 × 5y2 = 20 × 5 × x2 × y2 = 100 x2y2
Area of 4th rectangle = 4x × 3x2 = 4 × 3 × x × x2 = 12x3
Area of 5th rectangle = 3mn × 4np = 3 × 4 × m × n × n × p = 12mn2p
Complete the table of products.
|
| 2x | − 5y | 3x2 | − 4xy | 7x2y | − 9x2y2 |
| 2x | 4x2 | … | … | … | … | … |
| − 5y | … | … | − 15x2y | … | … | … |
| 3x2 | … | … | … | … | … | … |
| − 4xy | … | … | … | … | … | … |
| 7x2y | … | … | … | … | … | … |
| − 9x2y2 | … | … | … | … | … | … |
The table can be completed as follows.
|
| 2x | − 5y | 3x2 | − 4xy | 7x2y | − 9x2y2 |
| 2x | 4x2 | − 10xy | 6x3 | − 8x2y | 14x3y | − 18x3y2 |
| − 5y | − 10xy | 25 y2 | − 15x2y | 20xy2 | − 35x2y2 | 45x2y3 |
| 3x2 | 6x3 | − 15x2y | 9x4 | − 12x3y | 21x4y | − 27x4y2 |
| − 4xy | − 8x2y | 20xy2 | − 12x3y | 16x2y2 | − 28x3y2 | 36x3y3 |
| 7x2y | 14x3y | − 35x2y2 | 21x4y | − 28x3y2 | 49x4y2 | − 63x4y3 |
| − 9x2y2 | − 18x3y2 | 45 x2y3 | − 27x4y2 | 36x3y3 | − 63x4y3 | 81x4y4 |
Obtain the volume of rectangular boxes with the following length, breadth and height respectively.
(i) 5a, 3a2, 7a4 (ii) 2p, 4q, 8r (iii) xy, 2x2y, 2xy2
(iv) a, 2b, 3c
We know that,
Volume = Length × Breadth × Height
(i) Volume = 5a × 3a2 × 7a4 = 5 × 3 × 7 × a × a2 × a4 = 105 a7
(ii) Volume = 2p × 4q × 8r = 2 × 4 × 8 × p × q × r = 64pqr
(iii) Volume = xy × 2x2y × 2xy2 = 2 × 2 × xy ×x2y × xy2 = 4x4y4
(iv) Volume = a × 2b × 3c = 2 × 3 × a × b × c = 6abc
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) xy × yz × zx = x2y2z2
(ii) a × (− a2) × a3 = − a6
(iii) 2 × 4y × 8y2 × 16y3 = 2 × 4 × 8 × 16 × y × y2 × y3 = 1024 y6
(iv) a × 2b × 3c × 6abc = 2 × 3 × 6 × a × b × c × abc = 36a2b2c2
(v) m × (− mn) × mnp = − m3n2p
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