How do you factor #28m n ^ { 2} u ^ { 2} - 56m n ^ { 2} v ^ { 2} + 8n ^ { 3} u ^ { 2} - 16n ^ { 3} v ^ { 2}#?

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Answer 1 · 2018-01-24T13:26:21

See a solution process below:

First, group the terms in the expression as:

#(28mn^2u^2 - 56mn^2v^2) + (8n^3u^2 - 16n^3v^2)#

Next, factor each term as:

#([28mn^2 * u^2] - [28mn^2 * 2v^2]) + ([8n^3 * u^2] - [8n^3 * 2v^2]) =>#

#28mn^2(u^2 - 2v^2) + 8n^3(u^2- 2v^2)#

Now, factor out the common term in the two main terms of the expression:

#(28mn^2 + 8n^3)(u^2 - 2v^2)#

If necessary, we can also factor out common terms in the term on the left:

#([4n^2 * 7m] + [4n^2 * 2n])(u^2 - 2v^2) =>#

#4n^2(7m + 2n)(u^2 - 2v^2)#