Factorise with full method and explanation - (2a+b)^3+(a+2b)^3
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Step-by-step explanation:
(2a+b)³ + (a+2b)³
= (8a³+b³+3*4a²*b+3*2a*b²)+(a³+8b³+3*a²*2b+3a*4b²)
= 8a³+b³+12a²b+6ab²+a³+8b³+6a²b+12ab²
= 9a³+9b³+18a²b+18ab²
= 9(a³+b³)+18ab(a+b)
= 9(a+b)(a²-ab+b²) + 18ab(a+b)
= 9(a+b){a²-ab+b²+2ab}
= 9(a+b)(a²+ab+b²)
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