Question

Without actually calculating the cubes, find the value of (16)^3+(-7)^3+(-9)^3

Answer 1

the value i got was 3024

Answer 2

(16)^3 = (7 + 9)^3 = 7^3 + 9^3 + 3 x 7^2 x 9 + 3 x 9^2 x 7

=>(16)^3 + (-7)^3 + (-9)^3 = (-7)^3 + (-9)^3 + 7^3 + 9^3 + 3 x 7^2 x 9 + 3 x 9^2 x 7

= [(-7)^3 + 7^3] + [9^3 + (-9)^3] + 3 x 7^2 x 9 + 3x9^2x7

= 0 + 0 + 3 x 7^2 x 9 + 3 x 9^2 x 7

= 3 x 7^2 x 9 + 3 x 9^2 x 7

= 3 x 9 x 7 x (7 + 9)

= 3 x 7 x 9 x 16

= 3 x 7 x 9 x 8 x 2

= 6 x 7 x 8 x 9

= 3024

Hope this helps!

:)