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Question

Factorise 2(ab+cd)a2b2+c2+d2

A
(c+da+b)(c+dab)
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B
(c+d+a+b)(c+dab)
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C
(cd+a+b)(cdab)
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D
(c+d+ab)(cdab)
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Solution

The correct option is B (c+d+a+b)(c+dab)
2(ab+cd)a2b2+c2+d2
= 2ab+2cda2b2+c2+d2
Re-arranging the terms , we get
= c2+2cd+d2(a2+2ab+b2)
We know (a+b)2=a2+2ab+b2
= (c+d)2(a+b)2
This is of the form x2y2 where x=c+d and y=a+b
We know x2y2=(x+y)(xy)
= (c+d+a+b)(c+dab)

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