Question

L.C.M of (a³+b³) and (a⁴-b⁴)​

Answer 1

a³+b³ = (a+b) (a²-ab+b²)

a⁴+b⁴ = (a²-b²) (a²+b²)

= (a-b) (a+b) (a²+b²)

LCM = (a+b) (a-b)

(a²+b²) (a²-ab+b²)

= (a⁴-b⁴) (a²-ab+b²)

= (a³+b³) (a-b) (a²+b²)

Answer 2

$\sf{ a³+b³ = (a+b) (a²-ab+b²) }$

$\sf{ a+b \: \: \: = (a²-b²) (a²+b²) }$

$\sf{~~~~~~~~~~~~~= (a-b) (a+b) (a²+b²) }$

$\bf{LCM :- }$

$\bf{~~~~(a+b) (a-b) - (a²+b²) (a²-ab+b²)}$

$\sf{= (a^-b4) (a²-ab+b²)}$

$\sf{ = (a³+b³) (a-b) (a²+b²) }$

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