Question

factorise: 9x^3-1/3​

Answer 1

${\bf\huge\underline\purple{\underline\red{solution}}: - }$

$\tt\dashrightarrow{{9 {x}^{3} - \frac{1}{3} }} \\ \\ { \tt{now}} \\ \\ { \tt\dashrightarrow{ {(3)}^{2} {(x)}^{3} - \frac{1}{3} }} \\ \\ {\tt\dashrightarrow{ \frac{ {(3)}^{2} {(x)}^{3} \times 3}{3} - \frac{1}{3} }} \\ \\ {\tt\dashrightarrow{ \frac{ {(3)}^{3} {(x)}^{3} }{3} - \frac{1}{3} }} \\ \\ { \tt\dashrightarrow{ \frac{ {(3x)}^{3} - {1} }{3} }} \\ \\ {\tt{we \: know \: \:{1}^{3} = 1}} \\ \\ { \tt{so \: now}} \\ \\ { \tt\dashrightarrow{ \frac{ {(3x)}^{3} - {1}^{3} }{3} }} \\ \\ { \tt{we \: use \: formula \: for \: numerator}} \\ \\ { \tt \underline\purple{formula} : - } \\ \\ { \tt\red{ {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2}) }} \\ \\ { \tt{so}} \\ \\ { \tt\dashrightarrow{ \frac{(3x - 1)( {3x}^{2} + 3x \times 1 + {1}^{2} )}{3} }} \\ \\ { \tt\dashrightarrow{ \frac{(3x - 1)( 9 {x}^{2} + 3x + 1 )}{3} }} \\ \\ { \tt{we \: can \: write \: it \: as \: }} \\ \\ { \tt\dashrightarrow{ {(3x - 1)( 9 {x}^{2} + 3x + 1 )} = 3}} \\ \\ { \tt \underline\purple{i \: hope \: it \: helps \: you.}}$