1. If x = -2, y = 3 and z = 1, then the value of expression x3 + y3 + z3 – 3xyz is
(a) 38 (b) 37 (c) -37 (d) – 38
2. Degree of zero is ____
(a) 0 (b) 1 (c) 2 (d) not defined
3. By how much is a4 + 4a2b2 + b4 more than a4 -8a2b2 + b4?
(a) 12a2b2 (b) -12a2b2 (c) 2a4 + 2b4 (d) 10a2b2
4. If l = -1 and m = 2, then the value of 4l2 +9m2 +2lm – 9l2m is
(a) 39 (b) 24 (c) 18 (d) 36
Answers
Step-by-step explanation:
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★ Solution 1 :-
x³ + y³ + z³ - 3xyz
Substituting the values of x , y & z
→ ( - 2 )³ + 3³ + 1³ - 3[ - 2(3)(1) ]
→ - 8 + 27 + 1 - 3 [ -6 ]
→ 20 +18
→ 38
Hence , x³ + y³ - z³ - 3xyz = 38 , so option ( a ) is your answer.
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★ Solution 2 :-
Degree of zero is always zero .
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★ Solution 3 :-
We need to find , how much more is a⁴ + 4a²b² + b⁴ is greater than a⁴ - 8a²b² + b⁴.
To find , that firstly we need to subtract a⁴ + 4a²b² + b⁴ from a² - 8a²b² + b⁴
Now ,
→ a² + 4a²b² + b⁴ - [ a² - 8a²b² + b⁴ ]
→ a² + 4a²b² + b⁴ - a² + 8a²b² - b⁴
→ 4a²b² + 8a²b²
→ 12a²b²
Hence , a⁴ + 4a²b² + b⁴ is 12a²b² more than a⁴ - 8a²b² + b⁴ . So , option (b) is your answer .
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★ Solution 4 :-
4l² + 9m² + 2(lm) - 9(l²m)
Now , substituting the values of m & l
→ 4(-1)² + 9(2)² + 2[ ( - 1)(2) ] - 9[ ( -1)²(2) ]
→ 4( 1 ) + 9( 4 ) + 2 [ - 2] - 9[ ( 1 ) ( 2 ) ]
→ 4 + 36 - 4 - 18
→ 40 - 22
→ 18
Hence , 4l² + 9m² + 2lm - 9l²m = 18 . So , option ( c ) is your answer .