Question

FACTORISE
a³ -2√2b³​

Answer 1

Answer:

$a^3-2\sqrt{2}b^3=\bold{(a-b\sqrt{2})(a^{2}+2b^{2}+ab\sqrt{2})}$

Step-by-step explanation:

$a^3-2\sqrt{2}b^3 \\ \\ =a^3-(\sqrt{2}b\times\sqrt{2}b\times\sqrt{2}b)\\ \\= a^3 - (\sqrt{2}b)^{3} \\ \\ \\ \\ \text{Using the identity, }x^3-y^3=(x-y)(x^2+y^2+xy)\text{, we get...} \\ \\ a^3-2\sqrt{2}b^3=\bold{(a-b\sqrt{2})(a^{2}+2b^{2}+ab\sqrt{2})}$