Question

FACTORIZE:
${a}^{3} - {b}^{3} + 1 + 3ab$
please solve it fast,it's urgent

Answer 1

We know the formula

A^3 + B^3 + C^3 - 3ABC = (A+B+C)(A^2 + B^2 + C^2 - AB - BC - CA)

Here, in a^3 - b^3 + 1 + 3ab,
A = a
B = -b
c = 1

So we can factorise it using the formula as follows:

a^3 - b^3 + 1 + 3ab

= {a + (-b) + 1} {(a)^2 + (-b)^2 + (1)^2 - a×(-b) - (-b)×1 - a×1 }

= {a - b + 1} { a^2 + b^2 + 1 + ab + b - a }

= (a - b + 1) (a^2 + b^2 + 1 + ab + b - a)


Hope this helps!

Answer 2

I don't know.......