Factorise:

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

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Solution

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

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(2 a + 3 b)^{2} - 24 a b = (2 a - 3 b)^{2}

What is the LCM of $(2 a + 3 b)^{2}$ and $(4 a^{2} - 9 b^{2})$

2 a + 6 b - 3 (a + 3 b)^{2}

2 a + 6 b - 3 (a + 3 b)^{2}

= 2 (a + 3 b) - 3 (a + 3 b)^{2} [T a k i n g 2 c o m m o n f r o m 2 a + 6 b]

= (a + 3 b) {\begin{matrix} 2 - 3 (a + 3 b) \end{matrix}} [T a k i n g (a + 3 b) c o m m o n]

= (a + 3 b) (2 - 3 a - 9 b)

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

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

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