Question

factorise it propely:-

27(a+b)³- 64(a-b)³​

Answer 1

Answer:

The answer is $(7b-a)(37a^2+13b^2-14ab)$

Step-by-step explanation:

 $27(a+b)^3-64(a-b)^3$

$=3^3(a+b)^3-4^3(a-b)^3\\=(3(a+b))^3-(4(a-b))^3\\=(3a+3b)^3-(4a-4b)^3$

$=(3a+3b-(4a-4b))((3a+3b)^2+(3a+3b)(4a-4b)+(4a-4b)^3)\\=(3a+3b-4a+4b)(9a^2+9b^2+18ab+12a^2-12b^2+16a^2+16b^2-32ab)\\=(7b-a)(37a^2+13b^2-14ab)$

( using $x^3-y^3=(x-y)(x^2+xy+y^2)$ )