2011/069 ) Factor the following?

(x - 9753)(x -7531) + 234321

this can be factored by multiplying out and solving as quadratic however let is take x –a = t where a = (9753+7531)/2 = 8642

now 9753-8642 = 8642-7531 = 1111

so (x - 9753)(x -7531) + 234321
= (x-8642-1111)(x-8642 + 1111) + 234321
= (t-1111)(t+1111) + 234321 taking t = x- 8642
= t^2 – 1111^2 + 234321
= t^2- 1234321 + 234321
= t^2- 1000000
= t^2- 1000^2
= (t+1000)(t-1000)
= (x-8642+1000)(x-8642-1000)
= (x-7642)(x-9642)

This trick helps in keeping expression simple