Question

Find the value of 45³-25³-20³ without actually calculating the cubes

Answer 1

a+b+c=0 then a^3+b^3+c^3=3abc
here 45+(-20)+(-25)=0
hence  45³-25³-20³ =3*45(-25)*(-20)= 67500

Answer 2

Answer:

45³ - 25³ - 20³

Without actually calculating squares and cubes we do as:

a³ - b³ = (a+b)(a²+b²+ab)

(45-25)(45²+25²+45*25)  - 20³

20 (45²+25²+45*25)  - 20³

20 [ (45²+25²+45*25  - 20² ]            now take 25² - 20² is like a²-b²

20 [ 45² + 45*25 + (25-20)(25+20) ]

20 [ 45 (45 + 25 + 5 ) ]

20 *45 * 75

Step-by-step explanation: