Question

250(a-b)^3+2 factorise

Answer 1

$250 {(a - b)}^{3} + 2$
$250( {a}^{3} - {b}^{3} - 3 {a}^{2}b - 3 {b}^{2} a) + 2$
Taking 2 common
we get
2(125a^3-125b^3-375a^2b-375b^2a+1)
2({5a}^3-{5b}^3-3×25×5a^2 b-3×25×5b^2+1)
$2(( {5a + 5b)}^{3} + 1)$
2((5a+5b)^3 +1^3
by using identity A^3+b^3=(A+B)(A^2+ B^2 -AB)

you can factorise it

Answer 2

The answer is given below :

Now,

250(a - b)³ + 2

= 2[ 125(a - b)³ + 1 ]

= 2 [ 5³(a - b)³ + 1 ]

= 2 [ (5a - 5b)³ + 1³ ]

= 2 (5a - 5b + 1) { (5a - 5b)² - (5a - 5b)×1 + 1² }

= 2 (5a - 5b + 1) (25a² - 50ab + 25b² - 5a + 5b + 1),

which is the required factorization.

Thank you for your question.