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vesna_86 [32]
3 years ago
14

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

Mathematics
2 answers:
svlad2 [7]3 years ago
7 0

Answer:

(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!

:)

BartSMP [9]3 years ago
6 0
The value i got was 3024
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