Question

factorise (5a-4b)^3+(4b-3c)^3-(5a-3c)^3
be fast with steps​

Answer 1

$\bold{ \mathtt{ {(5a - 4b)}^{3} + {(4b - 3c)}^{3} + {(3c - 5a)}^{3}}}$

$\bold{ \mathtt{ \blue{put \: \: \: 5a - 4b = p}}} \\ \bold{ \mathtt{ \blue{ \: \: \: \: \: \: \: \: \: 4b - 3c = q}}} \\ \bold{ \mathtt{ \blue{ \: \: \: \: \: \: \: \: \: 3c - 5a = r}}} \\ \\ \bold{ \mathtt{ \blue{now \: \: \: \: \: \: \: p + q + r}}} \\ \bold{ \mathtt{ \blue{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 5a - 4b + 4b - 3c + 3c - 5a}}} \\ \bold{ \mathtt{ \blue{ = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}}$

$\bold{ \mathtt{ \green{{(5a - 4b)}^{3} + {(4b - 3c)}^{3} + {(3c - 5a)}^{3}}}} \\ \bold{ \mathtt{ \green{ = {p}^{3} + {q}^{3} + {r}^{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}} \\ \bold{ \mathtt{ \green{ = 3pqr \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}} \\ \bold{ \mathtt{ \green{ = 3(5a - 4b)(4b - 3c)(3c - 5a)}}}$

Answer 2

Answer:

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