Exercise 12.3 Page: 242
1. If m = 2, find the value of:
(i) m – 2
Solution:-
From the question it is given that m = 2
Then, substitute the value of m in the question
= 2 -2
= 0
(ii) 3m – 5
Solution:-
From the question it is given that m = 2
Then, substitute the value of m in the question
= (3 × 2) – 5
= 6 – 5
= 1
(iii) 9 – 5m
Solution:-
From the question it is given that m = 2
Then, substitute the value of m in the question
= 9 – (5 × 2)
= 9 – 10
= – 1
(iv) 3m2 – 2m – 7
Solution:-
From the question it is given that m = 2
Then, substitute the value of m in the question
= (3 × 22) – (2 × 2) – 7
= (3 × 4) – (4) – 7
= 12 – 4 -7
= 12 – 11
= 1
(v) (5m/2) – 4
Solution:-
From the question it is given that m = 2
Then, substitute the value of m in the question
= ((5 × 2)/2) – 4
= (10/2) – 4
= 5 – 4
= 1
2. If p = – 2, find the value of:
(i) 4p + 7
Solution:-
From the question it is given that p = -2
Then, substitute the value of p in the question
= (4 × (-2)) + 7
= -8 + 7
= -1
(ii) – 3p2 + 4p + 7
Solution:-
From the question it is given that p = -2
Then, substitute the value of p in the question
= (-3 × (-2)2) + (4 × (-2)) + 7
= (-3 × 4) + (-8) + 7
= -12 – 8 + 7
= -20 + 7
= -13
(iii) – 2p3 – 3p2 + 4p + 7
Solution:-
From the question it is given that p = -2
Then, substitute the value of p in the question
= (-2 × (-2)3) – (3 × (-2)2) + (4 × (-2)) + 7
= (-2 × -8) – (3 × 4) + (-8) + 7
= 16 – 12 – 8 + 7
= 23 – 20
= 3
3. Find the value of the following expressions, when x = –1:
(i) 2x – 7
Solution:-
From the question it is given that x = -1
Then, substitute the value of x in the question
= (2 × -1) – 7
= – 2 – 7
= – 9
(ii) – x + 2
Solution:-
From the question it is given that x = -1
Then, substitute the value of x in the question
= – (-1) + 2
= 1 + 2
= 3
(iii) x2 + 2x + 1
Solution:-
From the question it is given that x = -1
Then, substitute the value of x in the question
= (-1)2 + (2 × -1) + 1
= 1 – 2 + 1
= 2 – 2
= 0
(iv) 2x2 – x – 2
Solution:-
From the question it is given that x = -1
Then, substitute the value of x in the question
= (2 × (-1)2) – (-1) – 2
= (2 × 1) + 1 – 2
= 2 + 1 – 2
= 3 – 2
= 1
4. If a = 2, b = – 2, find the value of:
(i) a2 + b2
Solution:-
From the question it is given that a = 2, b = -2
Then, substitute the value of a and b in the question
= (2)2 + (-2)2
= 4 + 4
= 8
(ii) a2 + ab + b2
Solution:-
From the question it is given that a = 2, b = -2
Then, substitute the value of a and b in the question
= 22 + (2 × -2) + (-2)2
= 4 + (-4) + (4)
= 4 – 4 + 4
= 4
(iii) a2 – b2
Solution:-
From the question it is given that a = 2, b = -2
Then, substitute the value of a and b in the question
= 22 – (-2)2
= 4 – (4)
= 4 – 4
= 0
5. When a = 0, b = – 1, find the value of the given expressions:
(i) 2a + 2b
Solution:-
From the question it is given that a = 0, b = -1
Then, substitute the value of a and b in the question
= (2 × 0) + (2 × -1)
= 0 – 2
= -2
(ii) 2a2 + b2 + 1
Solution:-
From the question it is given that a = 0, b = -1
Then, substitute the value of a and b in the question
= (2 × 02) + (-1)2 + 1
= 0 + 1 + 1
= 2
(iii) 2a2b + 2ab2 + ab
Solution:-
From the question it is given that a = 0, b = -1
Then, substitute the value of a and b in the question
= (2 × 02 × -1) + (2 × 0 × (-1)2) + (0 × -1)
= 0 + 0 +0
= 0
(iv) a2 + ab + 2
Solution:-
From the question it is given that a = 0, b = -1
Then, substitute the value of a and b in the question
= (02) + (0 × (-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)
Solution:-
From the question it is given that x = 2
We have,
= x + 7 + 4x – 20
= 5x + 7 – 20
Then, substitute the value of x in the equation
= (5 × 2) + 7 – 20
= 10 + 7 – 20
= 17 – 20
= – 3
(ii) 3 (x + 2) + 5x – 7
Solution:-
From the question it is given that x = 2
We have,
= 3x + 6 + 5x – 7
= 8x – 1
Then, substitute the value of x in the equation
= (8 × 2) – 1
= 16 – 1
= 15
(iii) 6x + 5 (x – 2)
Solution:-
From the question it is given that x = 2
We have,
= 6x + 5x – 10
= 11x – 10
Then, substitute the value of x in the equation
= (11 × 2) – 10
= 22 – 10
= 12
(iv) 4(2x – 1) + 3x + 11
Solution:-
From the question it is given that x = 2
We have,
= 8x – 4 + 3x + 11
= 11x + 7
Then, substitute the value of x in the equation
= (11 × 2) + 7
= 22 + 7
= 29
7. Simplify these expressions and find their values if x = 3, a = – 1, b = – 2.
(i) 3x – 5 – x + 9
Solution:-
From the question it is given that x = 3
We have,
= 3x – x – 5 + 9
= 2x + 4
Then, substitute the value of x in the equation
= (2 × 3) + 4
= 6 + 4
= 10
(ii) 2 – 8x + 4x + 4
Solution:-
From the question it is given that x = 3
We have,
= 2 + 4 – 8x + 4x
= 6 – 4x
Then, substitute the value of x in the equation
= 6 – (4 × 3)
= 6 – 12
= – 6
(iii) 3a + 5 – 8a + 1
Solution:-
From the question it is given that a = -1
We have,
= 3a – 8a + 5 + 1
= – 5a + 6
Then, substitute the value of a in the equation
= – (5 × (-1)) + 6
= – (-5) + 6
= 5 + 6
= 11
(iv) 10 – 3b – 4 – 5b
Solution:-
From the question it is given that b = -2
We have,
= 10 – 4 – 3b – 5b
= 6 – 8b
Then, substitute the value of b in the equation
= 6 – (8 × (-2))
= 6 – (-16)
= 6 + 16
= 22
(v) 2a – 2b – 4 – 5 + a
Solution:-
From the question it is given that a = -1, b = -2
We have,
= 2a + a – 2b – 4 – 5
= 3a – 2b – 9
Then, substitute the value of a and b in the equation
= (3 × (-1)) – (2 × (-2)) – 9
= -3 – (-4) – 9
= – 3 + 4 – 9
= -12 + 4
= -8
8. (i) If z = 10, find the value of z3 – 3(z – 10).
Solution:-
From the question it is given that z = 10
We have,
= z3 – 3z + 30
Then, substitute the value of z in the equation
= (10)3 – (3 × 10) + 30
= 1000 – 30 + 30
= 1000
(ii) If p = – 10, find the value of p2 – 2p – 100
Solution:-
From the question it is given that p = -10
We have,
= p2 – 2p – 100
Then, substitute the value of p in the equation
= (-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?
Solution:-
From the question it is given that x = 0
We have,
2x2 + x – a = 5
a = 2x2 + x – 5
Then, substitute the value of x in the equation
a = (2 × 02) + 0 – 5
a = 0 + 0 – 5
a = -5
10. Simplify the expression and find its value when a = 5 and b = – 3.
2(a2 + ab) + 3 – ab
Solution:-
From the question it is given that a = 5 and b = -3
We have,
= 2a2 + 2ab + 3 – ab
= 2a2 + ab + 3
Then, substitute the value of a and b in the equation
= (2 × 52) + (5 × (-3)) + 3
= (2 × 25) + (-15) + 3
= 50 – 15 + 3
= 53 – 15
= 38