Question

factorise 64 a cube -27 b cube -144 a square b + 108 a b square

Answer 1

Here is your complete solution

Answer 2

Answer: Its factorised form is $(4a-3b)^3$

Step-by-step explanation:

Since we have given that

$64a^3-27b^3-144a^2b+108ab^2$

We need to factorise the above polynomial.

As we know the "Cubic identity":

$(a-b)^3=a^3-b^3+3ab(a-b)$

By applying this on the polynomial,we get,

$64a^3-27b^3-144a^2b+108ab^2\\\\(4a)^3-(3b)^3+3\times (4a)^2\times (3b)+3\times 4a\times (3b)^2\\\\=(4a-3b)^3$

Hence, its factorised form is $(4a-3b)^3$