Algebraic Expressions
Exercise 12.3
1). If m = 2, find the value of:
(i) m – 2 (ii) 3m – 5
(iii) 9 – 5m (iv) 3m2 – 2m – 7
(v) 5m/2 – 4
Solution:
(i) m – 2
Put m = 2 in the given expression
m – 2 = 2 – 2 = 0
(ii) 3m – 5
Put m = 2 in the given expression
3m – 5 = 3(2) – 5
= 6 – 5
= 1
(iii) 9 – 5m
Put m = 2 in the given expression
9 – 5m = 9– 5(2)
= 9 – 10
= –1
(iv) 3m2 – 2m – 7
Put m = 2 in the given expression
3m2 – 2m – 7 = 3(2)2 – 2(2) – 7
= 3(4) – 4 – 7
= 12 – 4 – 7
= 1
(v) 5m/2 – 4
Put m = 2 in the given expression
5m/2 – 4 =( 5 x 2/2 ) – 4
= (10/2 ) – 4
= 5 – 4
= 1
2). If p = – 2, find the value of:
(i) 4p + 7 (ii) – 3p2 + 4p + 7
(iii) – 2p3 – 3p2 + 4p + 7
Solution:
(i) 4p + 7
Put p = – 2 in the given expression
4p + 7 = 4(–2) + 7
= – 8 + 7
= – 1
(ii) – 3p2 + 4p + 7
Put p = – 2 in the given expression
– 3p2 + 4p + 7 = – 3(– 2)2 + 4(– 2) + 7
= – 3(4) – 8 + 7
= – 12 – 8 + 7
= – 13
(iii) – 2p3 – 3p2 + 4p + 7
Put p = – 2 in the given expression
– 2p3 – 3p2 + 4p + 7 = – 2(– 2)3 – 3(– 2)2 + 4(– 2) + 7
= – 2(– 8) – 3(4) – 8 + 7
= 16 – 12 – 8 + 7
= 3
3). Find the value of the following expressions, when x = –1:
(i) 2x – 7 (ii) – x + 2
(iii) x2 + 2x + 1 (iv) 2x2 – x – 2
Solution:
(i) 2x – 7
Put x = –1 in the given expression
2x – 7 = 2(– 1) – 7
= – 2 – 7
= – 9
(ii) – x + 2
Put x = –1 in the given expression
– x + 2 = – (–1)+ 2
= 1 + 2
= 3
(iii) x2 + 2x + 1
Put x = –1 in the given expression
x2 + 2x + 1 =(–1)2 + 2(–1) + 1
= 1– 2 + 1
= 0
(iv) 2x2 – x – 2
Put x = –1 in the given expression
2x2 – x – 2 = 2(–1)2 – (–1) – 2
= 2(1) + 1– 2
= 2 + 1 –2
= 1
4). If a = 2, b = – 2, find the value of:
(i) a2 + b2 (ii) a2 + ab + b2
(iii) a2 – b2
Solution:
(i) a2 + b2
Put a = 2, b = – 2 in the given expression
a2 + b2 = (2)2 + (– 2)2
= 4 + (4)
= 4 + 4
= 8
(ii) a2 + ab + b2
Put a = 2, b = – 2 in the given expression
a2 + ab + b2 = (2)2 + 2 X (– 2) + (– 2)2
= 4 + (– 4) + (4)
= 4 – 4 + 4
= 4
(iii) a2 – b2
Put a = 2, b = – 2 in the given expression
a2 – b2 = (2)2 – (– 2)2
= 4 – (4)
= 4 – 4
= 0
5). When a = 0, b = – 1, find the value of the given expressions:
(i) 2a + 2b (ii) 2a2 + b2 + 1
(iii) 2a2b + 2ab2 + ab (iv) a2 + ab + 2
Solution:
(i) 2a + 2b
Put a = 0, b = – 1 in the given expression
2a + 2b = 2(0) + 2(– 1)
= 0 – 2
= – 2
(ii) 2a2 + b2 + 1
Put a = 0, b = – 1 in the given expression
2a2 + b2 + 1 = 2(0)2 + (– 1)2 + 1
= 2(0) +(1) + 1
= 0 + 1 + 1
= 2
(iii) 2a2b + 2ab2 + ab
Put a = 0, b = – 1 in the given expression
2a2b + 2ab2 + ab = 2 X 02 X (– 1) + 2 X 0 X (– 1)2 + 0 X (– 1)
= 0 + 0 + 0
= 0
(iv) a2 + ab + 2
Put a = 0, b = – 1 in the given expression
a2 + ab + 2= 02 + 0 X (– 1) + 2
= 0 + 0 + 2
= 2
6). Simplify the expressions and find the value if x is equal to 2
(i) x + 7 + 4 (x – 5) (ii) 3 (x + 2) + 5x – 7
(iii) 6x + 5 (x – 2) (iv) 4(2x – 1) + 3x + 11
Solution:
(i) x + 7 + 4 (x – 5)
= x + 7 + 4x – 20
= x + 4x + 7 – 20
= 5x – 13
= 5(2) – 13 (putting x = 2 in the expression)
= 10 – 13
= – 3
(ii) 3 (x + 2) + 5x – 7
= 3x + 6 + 5x – 7
= 3x + 5x + 6 – 7
= 8x – 1
= 8 (2) – 1 (putting x = 2 in the expression)
= 16 – 1
= 15
(iii) 6x + 5 (x – 2)
= 6x + 5x – 10
= 11x – 10
= 11(2) – 10 (putting x = 2 in the expression)
= 22 – 10
= 12
(iv) 4(2x – 1) + 3x + 11
= 8x – 4 + 3x + 11
= 8x + 3x – 4 + 11
= 11x + 7
= 11(2) + 7 (putting x = 2 in the expression)
= 22 + 7
= 29
7). Simplify these expressions and find their values if x = 3, a = – 1,
b = – 2.
(i) 3x – 5 – x + 9 (ii) 2 – 8x + 4x + 4
(iii) 3a + 5 – 8a + 1 (iv) 10 – 3b – 4 – 5b
(v) 2a – 2b – 4 – 5 + a
Solution:
(i) 3x – 5 – x + 9
= 3x – x – 5 + 9
= 2x + 4
= 2 (3) + 4 (putting x = 3 in the expression)
= 6 + 4
= 10
(ii) 2 – 8x + 4x + 4
= 2 + 4 – 8x + 4x
= 6 – 4x
= 6 – 4(3)
= 6 – 12
= – 6
(iii) 3a + 5 – 8a + 1
= 3a – 8a + 5 + 1
= – 5a + 6 (putting a = –1 in the expression)
= – 5(–1) + 6
= 5 + 6
= 11
(iv) 10 – 3b – 4 – 5b
= 10 – 4 – 3b – 5b
= 6 – 8b
= 6 – 8(– 2) (putting b = –2 in the expression)
= 6 + 16
= 22
(v) 2a – 2b – 4 – 5 + a
= 2a + a – 2b – 4 – 5
= 3a – 2b – 9
= 3(–1) – 2(–2) – 9 (putting a = –1, b = –2 in the expression)
= – 3 + 4 – 9
= – 8
8). (i) If z = 10, find the value of z3 – 3(z – 10).
z3 – 3(z – 10) = z3 – 3z + 30
= (10)3 – 3(10) + 30
= 1000 – 30 + 30
= 1000
(ii) If p = – 10, find the value of p2 – 2p – 100
p2 – 2p – 100 = (–10)2 – 2(–10) – 100
= 100 + 20 – 100
= 20
9). What should be the value of a if the value of 2x2 + x – a equals to 5, when x = 0?
2x2 + x – a = 5 when x = 0
Put x = 0 in the above expression
2(0)2 +(0) – a = 5
2 X 0 + 0 – a = 5
0 + 0 – a = 5
– a = 5
a = – 5
10). Simplify the expression and find its value when a = 5 and
b = – 3.
2(a2 + ab) + 3 – ab
= 2a2 + 2ab + 3 – ab
= 2a2 + 2ab – ab + 3
= 2a2 + ab + 3
= 2(5)2 + 5 X ( – 3) + 3
= 2 (25) – 15 + 3
= 50 – 15 + 3
= 38
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