Question

216x^3 +1/27 by a3 +b3=a+b a2-ab+ab2​

Answer 1

$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \:SOLUTION\: \: \red{ \mid}}}}}}}}$

$\star \: \: \underline{ \bold{ \: To \: \: factorise \: \: : } \: } \: \: \: \bold{216x {}^{3} + \frac{1}{27} }$



$\to \: \: \underline{ \bold{ \: \: Formula \: \: used \: \: : }} \\ \\ \: \boxed{ \bold{ \: a {}^{3} + b {}^{3} = (a + b)(a {}^{2} - ab + b {}^{2} )}}$


$\bold{216x {}^{3} + \frac{1}{27} } \\ \\ \bold{ = (6x) {}^{3} + ( \frac{1}{3}) {}^{3} } \\ \\ \bold{ = (6x + \frac{1}{3})[(6x) {}^{2} - (6x \times \frac{1}{3} ) + ( \frac{1}{3}) {}^{2}]} \\ \\ \bold{ = (6x + \frac{1}{3} )(36x {}^{2} - 2x + \frac{1}{9}) }$



$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \: ANSWER \: \: \red{ \mid}}}}}}}}$

$\boxed{ \boxed{ \bold{ \pink{ \: \: 216x {}^{3} + \frac{1}{27} = (6x + \frac{1}{3} )(36x {}^{2} - 2x + \frac{1}{9} ) \: \: }}}}$