# Algebraic Expressions

## Exercise 9.2

Question 1: Find the product of the following pairs of monomials.

(i) 4, 7p

Answer: 4 xx 7 p = 28p

(ii) – 4p, 7p

Answer: - 4p xx 7p = -28p^2

(iii) – 4p, 7pq

Answer: - 4p xx 7pq = -28p^2q

(iv) 4p^3, – 3p

Answer: 4p^3q xx - 3p = -12p^4q

(v) 4p, 0

Answer: 4p xx 0 = 0

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)

(i) p xx q = pq

(ii) 10m xx 5n = 50mn

(iii) 20x^2 xx 5y^2 = 100x^2y^2

(iv) 4x \xx 3x^2 = 12x^3

(v) 3mn xx 4np = 12mn^2p

Question 3: Complete the following table of products:

Mononomials2x-5y3x2-4xy7x2y9x2y2
2x4x2-10xy6x3-8x2y14x3y-18x3y2
-5y-10xy25y2-15x2y20xy2-35x2245x2y3
3x26x3-15x2y9x4-12x3y21x4y-27x4y2
-4xy-8x2y20xy2-12x3y16x2y2-28x3y236x3y3
7x2y14x3y-35x2y221x4y-28x3y249x4y2-63x4y3
-9x2y2-18x3y245x2y3-27x4y236x3y3-63x4y381x4y4

Question 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^2y, 2xy^2(iv) a, 2b, 3c

(i) 5a \xx 3a^2 xx 7a^4 = 105a^7
(ii) 2p \xx 4q \xx 8r = 64pqr
(iii) xy \xx 2x^2y \xx 2xy^2 = 4x^4y^4
(iv) a \xx 2b \xx 3c = 6abc

Question 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

Answer: (i) x^2y^2z^2
(ii) –a^6
(iii) 1024y^6
(iv) 36a^2b^2c^2
(v) –m^3n^2p

### Exercise 9.3

Question 1: Carry out the multiplication of the expressions in each of the following pairs.

(i) 4p, q + r

Answer: 4p(q + r) = 4pq + 4pr

(ii) ab, a – b

Answer: ab(a - b) = a^2b - ab^2

(iii) a + b, 7a^2b^2

Answer: (a + b) (7a^2b^2) = 7a^3b^2 + 7a^2b^3

(iv) a^2– 9, 4a

Answer: (a^2 - 9)(4a) = 4a^3 - 36a^2

(v) pq + qr + rp, 0

Answer: (pq + qr + rp) xx 0 = 0

Question 2: Complete the table.

First expressionSecond expressionProduct
ab + c + dab + ac + ad
x + y - 55xy5x2y + 5xy2 - 25xy
p6p2 - 7p + 56p3 - 7p2 + 5p
4p2q2p2 - q24p4q2 - 4p214
a + b + cabca2bc + ab2c + abc2

Question 3: Find the product.

(i) a^2 xx (2a^22 xx (4a^26)

Answer: As you know; a^m \xx a^n \xx a^o = a^(m+n+o)

So, we get; a^2 xx 2a^22 xx 4a^26)= 8a^48

(ii) 2/3xy\xx(-(9)/(10)x^2y^2)

Answer: =-3/5x^3y^3

(iii) (10)/(3)pq^3\xx6/5p^3q

Answer: =-4p^4q^4

(iv) x \xx\ x^2 xx\ x^3 xx \x^8

Answer: = x^14

Question 4: (a) Simplify 3x (4x – 5) + 3 and find its values for (i) x = 3 (ii) x =1/2

Answer:(i) putting x = 3 in the equation we get
12x^2 - 15x + 3
= 108 - 45 + 3 = 66

(ii) putting x = 1/2 in the equation we get

12xx1/4-(15)/(2)+3=3-(15)/(2)+3=(15)/(2)

Question 4: (b) Simplify a (a^2+ a + 1) + 5 and find its value for (i) a = 0, (ii) a = 1 and (iii) a = – 1

Answer: a(a^2+a+1)
=a^3+a^2+a

(i) putting a= 0 in the equation we get
0^3 + 0^2 + 0 = 0

(ii) putting a = 1 in the equation we get
1^3+ 1^2+ 1 = 1 + 1 + 1 = 3

(iii) putting a = -1 in the equation we get
-1^3 + 1^2 -1 = -1 + 1 + 1 = 1

Question 5: (a) Add: p ( p – q), q ( q – r) and r ( r – p)

Answer:(p^2 - pq) + (q^2 - qr) + (r^2 - pr)
= p^2 + q^2 + r^2 - pq - qr - pr

(b) Add: 2x (z – x – y) and 2y (z – y – x)

Answer: (2xz - 2x^2- 2xy) + (2yz - 2y^2 - 2xy)
= 2xz - 4xy + 2yz - 2x^2 - 2y^2

(c) Subtract: 3l (l – 4 m + 5 n) from 4l ( 10 n – 3 m + 2 l )

Answer: (40ln - 12lm + 8l^2) - (3l^2 - 12lm + 15ln)
= 40ln - 12lm + 8l^2 - 3l^2 - 12lm + 15ln
= 55ln - 24lm + 5l^2

(d) Subtract: 3a (a + b + c ) – 2 b (a – b + c) from 4c ( – a + b + c )

Answer:= (-4ac + 4bc + 4c^2) - (3a^2 + 3ab + 3ac)
= -4ac + 4bc + 4c^2 - 3a^2 - 3ab - 3ac
= -7ac + 4bc + 4c^2 - 3a^2 - 3ab