(99)³
27y³+125z³
64m³+343n³
Answers
Answer:
see the solutions given below
Step-by-step explanation:
Solution 1:
(99)³ = (100-1)³
Using Identity, (a-b)³ = a³-b³-3ab(a-b)
= 100³-1³-3×100×1(100-1)
= 1000000 - 1 - 300 × 99
= 1000000 - 1 - 29700
= 1000000 - 29701
= 970299
Solution 2:
27y³+125z³ = (3y)³+(5z)³
Using Identity, (a)³ + (b)³ = (a+b)(a²+b²-2ab)
= (3y+5z) [ (3y)² + (5z)² - 2×3y×5z]
= (3y+5z) ( 9y² + 25z² - 30yz )
Solution 3:
64m³ + 343n³ = (4m)³ + (7n)³
Using Identity, (a)³ + (b)³ = (a+b)(a²+b²-2ab)
= (4m+7n) [ (4m)² + (7n)² - 2×4m×7n]. = (4m+7n) (16m² + 49n² - 56mn)
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solution by UTKARSH SHARMA from MICRO EDUCATION
Answer:
(99)³ = (100-1)³
Using Identity, (a-b)³ = a³-b³-3ab(a-b)
= 100³-1³-3×100×1(100-1)
= 1000000 - 1 - 300 × 99
= 1000000 - 1 - 29700
= 1000000 - 29701
= 970299
(i) 27y 3 + 125z 3 = (3y)3 + (5z)3 = (3y + 5z) (3y)2 − (3y)(5z) + (5z)2
= (3y + 5z)(9y 2 − 15yz + 25z 2)
(ii) 64m 3 − 343n 3 = (4m)3 − (7n)3 = (4m − 7n) (4m)2 + (4m)(7n) + (7n)2
= (4m − 7n)(16m 2 + 28mn + 49n 2)
Step-by-step explanation: