Question

factorise (a+b)^3 - (a-b)^3

Answer 1

$\textbf{ Hello Mate! }$

${x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} ) \\ \\ {(a + b)}^{3} - {(a - b)}^{3}$

Hence, we will use same method to solutions.

= ( a + b )^3 - ( a - b )^3

= [ (a+b)-(a-b )][(a-b)^2+(a+b)(a-b)+(a-b)^2]

= [a+b-a+b][a^2+b^2+2ab+a^2-b^2+a^2+b^2-2ab ]

= 2b( 3a^2+ b^2 )

$\textsf{ \red{ = 2b( 3{a}^{2} + {b}^{2} )}}$

Have great future ahead!