Question

is this how it's taken common , and arrive at the answer?! ​

Answer 1

What you have done is correct. But you can just cancel the 2 and -2 on both sides instead of writing it as fraction and then cancelling.

[2x - 2a] [-2b] = [2y - 2b] [-2a]

● Take 2 common from [2x - 2a] and [2y - 2b] and cancel the 2 on both sides.

=> 2[x - a] [-2b] = 2[y - b] [-2a]

=> [x - a] [-2b] = [y - b] [-2a]

● Take -2 common from [-2b] and [-2a] and cancel the -2 on both sides

=> [x - a] (-2) [b] = [y - b] (-2) [a]

=> [x - a] [b] = [y - b] [a]

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Or you can simply take the 2 common on both sides and then cancel the 2 and also the -2.

$[2x - 2a] [-2b] = [2y - 2b] [-2a] \\ \\2 [x - a] [-2b] = 2[y - b] [-2a] \\ \\ \cancel2 [x - a] [ - 2b] = \cancel2[y - b] [-2a] \\ \\ [x - a] [ \cancel{ - 2} \: b] = [y - b] [\cancel{ - 2} \: a] \\ \\ [x - a] [b] = [y - b] [a]$