Question

উৎপাদকে বিশ্লেষণ কর: $8a^3+\frac{b^3}{27}$

Answer 1

$8a^3+\frac{b^3}{27}$

$=\left(2a\right)^3+\left(\frac{b}{3}\right)^3$

$=\left(2a+\frac{b}{3}\right)$$\left\lbrace\left(2a\right)^2-2a\cdot\frac{b}{3}+\left(\frac{b}{3}\right)^2\right\rbrace$

$=\left(2a+\frac{b}{3}\right)$$\left(4a^2-\frac{2ab}{3}+\frac{b^2}{9}\right)$

$=\left(\frac{6a+b}{3}\right)$$\left(\frac{36a^2-6ab+b^2}{9}\right)$

$=\frac13\left(6a+b\right)$$\cdot\frac19\left(36a^2-6ab+b^2\right)$

$=\frac{1}{27}\left(6a+b\right)$$\left(36a^2-6ab+b^2\right)$ [Answer]

Comments

Rules Applied :

• $a^3+b^3=(a+b)(a^2-ab+b^2)$