Factorise : 1/64a^3 - 1/16a^2b + 1/12ab^2 -1/24b^3

Question

Factorise : \(\frac{1}{64}a^3 - \frac1{16}a^2b+\frac1{12}ab^2-\frac{1}{27}b^3\)

Answer 1

\(\frac{1}{64}a^3 - \frac1{16}a^2b+\frac1{12}ab^2-\frac{1}{27}b^3\) 

= \(\big(\frac14a\big)^3\) - 3 x \(\big(\frac14a\big)^2\) x \(\frac13b\) + 3 x \(\frac14a\) x \(\big(\frac13b\big)^2\) - \(\big(\frac13b\big)^3\)

[∴ (a - b)³ = a³ - 3a²b + 3ab² - b³]

= \(\bigg(\frac14a-\frac13b\bigg).\)