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Question

Simplify:
[(5z2)2+40z]÷(5z+2)


A

2z+5

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B

2z5

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C

5z2

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D

5z+2

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Solution

The correct option is D

5z+2


To simplify :
[(5z2)2+40z]÷(5z+2)

Using the identity,
a22ab+b2=(ab)2 ,
[(5z2)2+40z]
=[25z220z+4+40z]
=[25z2+20z+4]

On factorizing,
25z2+20z+4,
we get,
25z2+20z+4
=(5z)2+2×(5z)×2+22

On applying the identity, a2+2ab+b2=(a+b)2,
we get ,
25z2+20z+4=(5z+2)2

So,
[((5z2)2+40z)(5z+2)]=(5z+2)2(5z+2)=5z+2


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