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4x^(2) + 28xy + 49y^(2) ->
(2x)^(2) + 28xy + (7y)^2
Split into brackets
( 2x + 7y)(2x + 7y)
If you applyuFOIL you will find toy come to '28xy'.
The clue to this problem is to note that '4' ^ '49' are both squared numbers.
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How do you factor the perfect trinomial?
Do you mean some thing like 4x2 - 28xy + 49y2 ? notice 4x2 = (2x)2 and 49y2 = either (7y)2 or (-7y)2 (1st and last terms must be squares) and the middle term is 2(2x)(-7y) (2 times sq root of 1st times sq root of last) Once the pattern is recognized: (sq root 1st + sqroot 2nd)2 or (sq root 1st - sqroot 2nd)2 depending on if middle term is positive or negative. So, back to my example: 4x2 - 28xy + 49y2 = (2x - 7y)2 because middle is negative. Simpler example factor x2 + 6x + 9. 1st and last are both squares sq root of 9 = 3 3 times 2 = 6 that fits the middle so x2 + 6x + 9 = (x + 3)2
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