Question

Factorise (2a+3b)^3-(2a-3b)^3

Answer 1

Ok here is your answer

Answer 2

Answer:

$18b(4 {a}^{2} + 3 {b}^{2})$

Solution:-

We have

${(2a + 3b)}^{3} - {(2a - 3b)}^{3}$

${(x}^{3} - {y}^{3})$

Where 2a+3b=x and 2a-3b=y

$(x - y)( {x}^{2} + xy + {y}^{2})$

$(x - y) {(x + y)}^{2} - xy$

$6b \times ({4a)}^{2} - ({4a}^{2} - {9b}^{2})$

As x-y=6b,x+y=4a and xy=4a^2-8b^2

$6b \times {(12a}^{2} + {9b}^{2})$

$18b( {4a}^{2} + {3b}^{2})$

Therefore,

${(2a + 3b)}^{2} - {(2a - 3b)}^{2} = 18b {(4a}^{2} + {3b}^{2})$