Question

Factorise:
(2a+b)^3+(a+2b)^3

Answer 1

According to x³ + y³ = (x + y)(x² - xy + y²),

    

$(2a+b)^3+(a+2b)^3 \\ \\ (2a+b+a+2b)((2a+b)^2-((2a+b) \cdot (a+2b))+(a+2b)^2) \\ \\ (3a+3b)(4a^2+4ab+b^2-(2a^2+4ab+ab+2b^2)+a^2+4ab+4b^2) \\ \\ 3(a+b)(4a^2+4ab+b^2-2a^2-5ab-2b^2+a^2+4ab+4b^2) \\ \\ 3(a+b)(3a^2+3ab+3b^2) \\ \\ 9(a+b)(a^2+ab+b^2)$

$\therefore\ (2a+b)^3+(a+2b)^3 \ = \ 9(a+b)(a^2+ab+b^2)$

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Answer 2

Step-by-step explanation:

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