Question

Without calculating the cube find the value of 75cube -25cube-50cube

Answer 1

$(75) {}^{3} + ( - 25) {}^{3} + ( - 50) {}^{3} \\ if \: 75 - 25 - 50 = 0 \\ \: \: \: 75 - 75 = 0 \\following \: the \: formula \: if \: a + b + c = 0 \\ then \: a {}^{3} + b {}^{3} + c {}^{3} = 3abc \\ so \: 75 {}^{3} - 25 {}^{3} - 50 {}^{3} = 3 \times 75 \times - 25 \times - 50 \\ so \: 75 {}^{3} - 25 {}^{3} - 50 {}^{3} = 281250$