How to factor $4d^2 -16w^2 -4cd+c^2$ ( from Hart William L., Intermediate Algebra, 1948)

algebra-precalculus soft-question quadratics factoring

I found this factoring problem in Hart, Intermediate Algebra, 1948, page $97$ , problem $n° 60$, ( at Archive.org).

Link :https://archive.org/details/intermediatealge030183mbp/page/n110/mode/1up

I tried to manipulate the formula using: $m^2n^2 = (mn)^2$ and also : $n^2 - m^2 = (m-n) ( m+n)$; I made use of addition's associativity and commutativity in order to exchange the order of the terms; but it led nowhere.

Any hint will be appreciated.

Thanks in advance

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Solution 1:

Hint: $4d^2-4dc + c^2 = (2d-c)^2$

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