How to factorise $(x+5)(x+9)(x+3)(x+7)-33$ ?

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Answer 1 · 2018-06-04T16:42:59

$rarr(x+5)(x+9)(x+3)(x+7)-33$

$=(x+3)(x+9)(x+7)(x+5)-33$

$=[x(x+9)+3(x+9)][x(x+5)+7(x+5)]-33$

$=[x^2+9x+3x+27][x^2+5x+7x+35]-33$

$=[x^2+12x+27][x^2+12x+35]-33$

$=[a+27][a+35]-33$

$=a(a+35)+27(a+35)-33$

$=a^2+35a+27a+945-33$

$=a^2+62a+912$

$=a^2+24a+38a+912$

$=a(a+24)+38(a+24)$

$=(a+24)(a+38)=[x^2+12x+24][x^2+12x+38]$

How to factorise (x+5)(x+9)(x+3)(x+7)-33(x+5)(x+9)(x+3)(x+7)-33?