Factor 81p^4-126p^3+49p^2

Math
81p4-126p3+49p2
Factor p2 out of 81p4-126p3+49p2.
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Factor p2 out of 81p4.
p2(81p2)-126p3+49p2
Factor p2 out of -126p3.
p2(81p2)+p2(-126p)+49p2
Factor p2 out of 49p2.
p2(81p2)+p2(-126p)+p2⋅49
Factor p2 out of p2(81p2)+p2(-126p).
p2(81p2-126p)+p2⋅49
Factor p2 out of p2(81p2-126p)+p2⋅49.
p2(81p2-126p+49)
p2(81p2-126p+49)
Factor using the perfect square rule.
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Rewrite 81p2 as (9p)2.
p2((9p)2-126p+49)
Rewrite 49 as 72.
p2((9p)2-126p+72)
Check the middle term by multiplying 2ab and compare this result with the middle term in the original expression.
2ab=2⋅(9p)⋅-7
Simplify.
2ab=-126p
Factor using the perfect square trinomial rule a2-2ab+b2=(a-b)2, where a=9p and b=-7.
p2(9p-7)2
p2(9p-7)2
Factor 81p^4-126p^3+49p^2

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