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If ac = cd = k, find the value of ...

If ac = cd = k, find the value of 3a2ac+c23b2bd+d2

A.

3k2

B.

2k - k2

C.

3b2k2bk2d+dk23b2bd+d2

D.

k2

Correct answer is C

ac = cd = k

ab = bk

cd = k

∴ c = dk

= 3a2ac+c23b2bd+d2

= 3(bk)2(bk)(dk)+dk23b2bd+a2

= 3b2k2bk2d+dk23b2bd+d2

k = 3b2k2bk2d+dk23b2bd+d2