Question

factorize a³-b³+1+3ab

Answer 1

Hello,

The identity used in the question is

${a}^{3 } + {b}^{3} + {c}^{3} - 3abc \\ = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca)$
Now,. The question is changes into the above form.

${a}^{3} - {b}^{ 3} + {1}^{3} - 3ab \times 1$
So changing into other
That is factorization of term is

$(a - b + c)( {a}^{2} + {( - b)}^{2} + {1}^{2} - a( - b) \\ - ( - b) \times 1 - 1 \times a \\ \\ = (a - b + c)( {a}^{2} + {b}^{2} + 1 + ab + b - a)$
So
The factorization is done by using the identity


Hope this will be helping you ✌️