Question

Write the terms of the following expressions:
(a) 9a+c+d-e
(b) 2m+n

Answer 1

Answer:

$(a) \: 9a + c + d + e \\ terms \: are \: \\ 9a \\ c \\ d \\ e \\ \\ \\ (b) \: 2m + n \\ terms \: are \\ 2m \\ n$

Answer 2

x

4. (a) Subtract 4a – 7ab + 3b + 12

from 12a – 9ab + 5b – 3

(b) Subtract 3xy + 5yz – 7zx

from 5xy – 2yz – 2zx + 10xyz

(c) Subtract 4p2q – 3pq + 5pq2 – 8p + 7q – 10

from 18 – 3p – 11q + 5pq – 2pq2 + 5p2q.

Sol. Rearranging the terms of the given expressions, changing the sign of each term of the expression to be subtracted and adding the two expressions, we get.

(b) Rearranging the terms of the given expressions, changing the sign of each term of the expression to be subtracted and adding the two expressions, we get.

(c) Rearranging the terms of the given expressions, changing the sign of each term of the expression to be subtacted and adding the two expressions, we get.

EXERCISE : 9.2

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

Sol. (i) 4 × 7p = (4 × 7) × p = 28p

(ii) – 4p × 7p = (– 4 × 7) × (p × p)

= 28 p1+1

= 28p2q

(iii) –4p × 7pq = (–4 × 7) × (p × p × q)

= – 28p1+1q

= – 28p2q

(iv) 4p3 × (–3p) = {4 × (–3)} × (p3 × p)

= – 12 × p3+1

= –12p4

(v) 4p × 0 = (4 × 0) × (p)

= 0 × p

= 0.

2. 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)

Sol. We know that the area of a rectangle = l × b, where l = length and b = breadth.

Therefore, the areas of rectangles with pair of monomials (p, q); (10m, 5n); (20x2, 5y2);

(4x, 3x2) and (3mn, 4np) as their lengths and breadths are given by

p × q = pq

10m × 5n = (10 × 5) × (m × n) = 50mn

20x2 × 5y2 = (20 × 5) × (x2 × y2)

= 100x2y2

4x × 3x2 = (4 × 3) × (x × x2)

= 12x3

and, 3mn × 4np = (3 × 4) × (m × n × n × p)

= 12mn2p

3. Complete the table of products:

Sol. Complete table is as under:

4. 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

Sol. (i) Required volume = 5a × 3a2 × 7a4

= (5 × 3 × 7) × (a × a2 × a4)

= 105a1+2+4 = 105a7

(ii) Required volume = 2p × 4q × 8r

= (2 × 4 × 8) × (p × q × r)

= 64 pqr.

(iii) Required volume = xy × 2x2y × 2xy2

= (1 × 2 × 2) × (xy × x2y × xy2)

= (4) × (x1+2+1 × y1+1+2)

= 4x4y4

(iv) Required volume = a × 2b × 3c

= (1 × 2 × 3) × (a × b × c)

= 6abc

(i) (a2) × (2a22) × (4a26)

(iv) x × x2 × x3 × x4

Sol. (i) (a2) × (2a22) × (4a26)

= (1 × 2 × 4) × (a2 × a22 × a26)

= 8a2 + 22 + 26 = 8a50