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Without actually calculating cubes find the value of25^3 -75^3+50^3. Please answer how to do it??

Without actually calculating cubes find the value of25^3 -75^3+50^3.
 Please answer how to do it??
 

Grade:9

1 Answers

Om Raga Datta
111 Points
3 years ago
Dear student, 
 
(a-b)= a3-b3-3ab(a-b)  
From this formula we can say that
a3-b3=   (a-b)+3ab(a-b)
25^3 -75^3+50^3 can be written as 25^3 -(75^3-50^3)
= 253-((75-50)3+3(75)(50)(75-50)
=253-253-3(75)(50)(25)
=  – 3(75)(50)(25)
= – 3(25)(3)(25)(2)(25)
=  – (3*3*2)(25)3
=  – (18)(15625)
=  – 281250
So the value of 25^3 -75^3+50^3 is – 281250
I hope that this solution would help you.
 
Raga datta

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