Question

8-a^3+3a^b-3ab^2+b^3

Answer 1

$8 - {a}^{3} + 3 {a}^{2} b - 3a {b}^{2} + {b}^{3} \\ {(2)}^{3} + {( - a)}^{3} + 3 {( - a)}^{2} b + 3( - a) {b}^{2} + {b}^{3}$
as you can see that the expression after 2 cube equals to cube of -a+b

${2}^{3} + {( - a + b)}^{3} \\ = {2}^{3} + {( b- a)}^{3}$
Now that our expession is in the form of acube + b^3 so we'll use an identity here,
${x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )$



so it becomes,
$(2 + b - a)( {2}^{2} - (2)(b - a) + {(b - a)}^{2})\\( - a + b + 2)(4 -2(b - a)+{a}^{2}-2ab+ {b}^{2})$