unit# 4 algebraic expressions and algebraic formulas exercise 4.1
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Mudassar Nazar Notes Published by Asghar Ali Page 1
Unit# 4 Algebraic Expression and Algebraic Formulas
Exercise 4.1
Question # 3 Reduce the following rational expressions to the lowest form:
(iv) .
Solution
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(v)
Solution
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(vi)
Solution
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(vii)
Solution
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= 4x ( x – 1 )
(viii)
Solution
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= x2 + 3x – 4
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Question # 5 Perform the indicated operation and simplify:
(iv) - -
Solution
- -
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(v) -
Solution
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(vi) - - -
Solution
- - -
= [ - ] – [ - ]
= – [ ]
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Exercise 4.4
Question # 1
Rationalize the denominator of the following:
(i)
Solution
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(ii)
Solution
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(iii)
Solution
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(iv)
Solution
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= ( 3 -2 )
(v)
Solution
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= + 4
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(vi)
Solution
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= +
(vii)
Solution
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(viii)
Solution
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Question # 3
If x + = 3, find (i) x2 + , (ii) x4 +
Solution
x + = 3
(x + )2 = (3)2
x2 + + 2 = 9
x2 + = 9 – 2
x2 + = 7
(x2 + )2 = (7)2
X4 + + 2 = 49
X4 + = 49 – 2
X4 + = 47
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Question # 4
If x - = 2, find (i) x2 + , (ii) x4 +
Solution
x - = 2
(x - )2 = (2)2
x2 + - 2 = 4
x2 + = 4 + 2
x2 + = 6
(x2 + )2 = (6)2
X4 + + 2 = 36
X4 + = 36 - 2
X4 + = 34
Question # 5
(ii) If x = , find the value of x + , and
Solution
x =
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x + = +
x + =
x + =
x + =
x + =
x + =
x + =
(x + )2 =( )2
x2 + + 2 =
x2 + = – 2
x2 + =
x2 + =
(x + )3 =( )3
x3 + + 3(x + ) =
x3 + + 3( ) =
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x3 + + 14 =
x3 + = - 14
x3 + =
x3 + =
Question # 6
If p = 2+ , find (i) p + , (ii) p - , (iii) p2 +
Solution
p = 2+
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= 2 -
(i) p + = 2 + + 2 -
p + = 4
(ii) p - = 2 + - ( 2 - )
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p - = 2 + + 2 +
p - = 2
(iii) (p + )2 = (4)2
P2 + + 2 = 16
P2 + = 16 – 2
P2 + = 14
(iv) P2 - = (p + ) (p - )
P2 - = (4) (2 )
P2 - =
Question # 7
If q = + 2, find (i) q + , (ii) q - , (iii) q2+ , (iv) q2-
Solution
q = + 2
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(i) q + = +
q + = 2
(ii) q - = -( )
q - = -
q - = 4
(iii) (q + )2 = (2 )2
q2+ + 2 = 4 5
q2+ + 2 = 20
q2+ = 20 – 2
q2+ = 18
(iv) q2- = (q + ) (q - )
q2- = ) (4)
q2- = 8