Question

$8(a + b) ^3 + c^3 \: resolve \: into \: factors$
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Answer 1

$a^3+b^3=(a+b)(a^2-ab+b^2)$

$8(a+b)^3+c^3=\\(2(a+b))^3+c^3=\\(2(a+b)+c)(4(a+b)^2-2(a+b)\cdot c+c^2))=\\(2a+2b+c)(4(a^2+2ab+b^2)-2ac-2bc+c^2)=\\(2a+2b+c)(4a^2+8ab+4b^2-2ac-2bc+c^2)=\\(2a+2b+c)(4a^2+8ab-2ac+4b^2-2bc+c^2)$