Question

Find the value of (5a-7b)^3+(9c-5a)^3+(7b-9c)^3

Answer 1

we have, (5a-7b)^3+(9c-5a)^3+(7b-9c)^3
Let us consider A = (5a-7b)
B = (9c-5a)
C = (7b-9c)
Now, A+B+C = (5a-7b)+(9c-5a)+(7b-9c) = 0
Since, A+B+C= 0
then, A^3 + B^3 + C^3 = 3ABC

This means,
(5a-7b)^3+(9c-5a)^3+(7b-9c)^3
= 3ABC
= 3 {(5a-7b)(9c-5a)(7b-9c)}

Answer 2

Hey friend,
Here is the answer:
$( {5a - 7b})^{3} + ( {9c - 5a})^{3} \\ + ( {7b - 9c})^{3} \\ \\ = ( {5a})^{3} - ( {7b})^{3} - 3 \times 5a \times 7b(5a - 7b) \\ + ( {9c})^{3} - ( {5a})^{3} - 3 \times 9c \times 5a(9c - 7b) \\ + ( {7b})^{3} - ( {9c})^{3} - 3 \times 7b \times 9c(7b - 9c) \\ \\ = {125a}^{3} - {343b}^{3} - 105ab \times 5a + 105ab \times 7b \\ + {729c}^{3} - {125a}^{3} - 135ac \times 9c + 135ac \times 5a \\ + {343b}^{3} - {729c}^{3} - 189bc \times 7b + 189bc \times 9c \\ \\ = {125a}^{3} - {343b}^{3} - {525a}^{2} b + {735ab }^{2} \\ + {729c}^{3} - {125a}^{3} - {1215ac}^{2} + {675a}^{2} c \\ + {343b}^{3} - {729c}^{3} - {1323b}^{2} c + {1701bc}^{2} \\ \\ after \: solving \\ \\ { - 525a}^{2} b \: + {735ab}^{2} - {1215ac}^{2} + {625a}^{2} c - {1323b}^{2} c + {1701bc}^{2}$
Hope my answer would be helpful to you!!!

And if helpful, then please mark as brainliest.

@Mahak24

Thanks...
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