Math Quiz Solution
Solution of Quiz
Grade: VII
Subject: Mathematics
Group-A (CQ)
1. A = x² + xy +
y², B = x − y, C = (x + y)(x² − xy + y²)
(a) Multiply 2a³
− b³ + 3abc by a⁴b²:
Solution:
(2a³ − b³ + 3abc)
× a⁴b²
= 2a⁷b² − 
+ 3a⁵b³c
Ans: 2a⁷b² − 
+ 3a⁵b³c
(b) Prove that AB
= x³ − y³:
Proof:
A = x² + xy + y²,
B = x − y
AB = (x² + xy + y²)(x − y)
= x³ − y³
(Proved)
(c) Find (AB)C:
Solution:
Given,
A = x² + 
+ y², B = x – y, C = (x + y)(x² − 
+ y²)
From (b) we have,
Now,
(x³ − y³)(x + y)(x² − xy +
y²)
(x³ − y³)
=
x⁶ − y⁶
Ans: x⁶ − y⁶
2. P = 2y² + 3y −
4, Q = 3y² − 4y − 5, R = 3x² + 5xy + 2y²
(a) Multiply
−2c²d² + 3d³c − 5cd² by −7c³d⁵:
Solution:
(−2c²d² + 3d³c − 5cd²) × (−7c³d⁵)
= 14c⁵d⁷ − 21c⁴d⁸
+ 35c⁴d⁷
Ans: 14c⁵d⁷ −
21c⁴d⁸ + 35c⁴d⁷
(b) Find P × Q:
= (2y² + 3y − 4)
(3y² − 4y − 5)
Ans: 6y⁴ + y³ − 34y² + y + 20
(c) Find (P − Q) × R
Solution:
Given,
P = 2y² + 3y − 4, Q = 3y² − 4y − 5, R = 3x² + 5xy + 2y²
= (−y² + 7y + 1)(3x² + 5xy + 2y²)
= −3x²y² + 21x²y
+ 3x² − 5xy³ + 35xy² + 5xy − 2y⁴ + 14y³ + 2y²
Ans: −3x²y² +
21x²y + 3x² − 5xy³ + 35xy² + 5xy − 2y⁴ + 14y³ + 2y²
3. A = 2x⁴ + 110
− 48x, B = 4x + 11 + x², C = 81p⁴ + q⁴ − 22p²q², D = 9p² + 2pq − q²
(a) Divide 36x³ +
9x² by 9x:
Solution:
(b) Divide A by B:
Solution:
Now,
Ans: 2x² − 8
(Quotient)
(c) Find C ÷ D:
Solution:
(81p⁴ + q⁴ − 22p²q²) ÷ (9p² + 2pq − q²)
Now,
= 9p² − 2pq - q²
(Quotient)
Group-B (Short
Question)
1. Multiply (x² −
x + 1) by (1 + x + x²):
Ans: 
2. Divide x⁴ − 1
by x² + 1:
(x⁴ − 1)
(x² + 1)
Now,
Ans: 
3. Divide 16x⁴ +
36x² + 81 by 4x² − 6x + 9:
Solution:
Now,
Ans: 
4. Multiply x² −
2xy + y² by x − y:
Solution:
5. Show that (x +
y)(x − y)(x² + y²) = x⁴ − y⁴
Proof:
(Proved)
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