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Math Assignment Class VIII | Algebraic Identities Ch-7
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Mathematics Assignment Class VIII
Algebraic Identities
Download or Print, free assignment with answer key for Class 8 on ALGEBRAIC IDENTITIES. Important and extra questions that cover all topics of ALGEBRAIC IDENTITIES and is useful and helpful for the students.
Algebraic Identities required to solve this assignment
Students need to learn these algebraic identities before start this assignment
(a + b)2 = a2 + b2 + 2ab
(a - b)2 = a2 + b2 - 2ab
a2 - b2 = (a + b)(a - b)
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
4(x + y)2 – 28(x2 –
y2) + 49(x – y)2
= [2(x
+ y)]2 – 2 x 2(x + y) x 7(x + y) + [7(x - y)]2
Using: a2 - 2ab + b2 = (a - b)2
we get
=
[2(x + y) – 7(x - y)]2.
=
(2x + 2y - 7x + 7y)2.
=
(- 5x + 9y)2 or (5x - 9y)2
x2 – 91 = 2.3 x 2.3 + 2 x 0.7 x 2.3 + 0.7 x 0.7
Ans: 10
Solution Hint
x2 – 91 = 2.3 ✕ 2.3 + 2 ✕ 0.7 ✕ 2.3 + 0.7 ✕ 0.7
= (2.3)2 + 2 ✕ 2.3 ✕ 0.7 + (0.7)2
= (2.3 + 0.7)2 = (3)2 = 9
x2 – 91 = 9
x2 = 9 + 91 = 100
x = 10
Answer: - 60xy + 20x
Solution Hint
(5x - 3y + 1)2 - (5x + 3y - 1)2.
Using a2 – b2
= (a + b)(a - b) we get
= (5x - 3y + 1+5x + 3y - 1)(5x - 3y + 1-5x - 3y + 1)
= (10x)(- 6y + 2) = - 60xy + 20x
Question 25:
If 3p - 4q = 8 and pq = 2, find the value of (3p - 4q)2.
Answer: 160
Solution Hint:
3p - 4q = 8
Squaring on both side we get
(3p – 4q)2 = 82
9p2 + 16q2 – 24pq = 64
9p2 + 16q2 – 24 🇽 2 = 64
9p2 + 16q2 – 48 = 64
9p2 + 16q2 = 64 + 48 = 112
(3p – 4q)2 = 9p2 + 16q2 + 24pq
= 112 + 24 🇽 2 = 160
Factorise :
Answer
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