Factor 3t^5-48tu^4

Math
3t5-48tu4
Factor 3t out of 3t5-48tu4.
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Factor 3t out of 3t5.
3t(t4)-48tu4
Factor 3t out of -48tu4.
3t(t4)+3t(-16u4)
Factor 3t out of 3t(t4)+3t(-16u4).
3t(t4-16u4)
3t(t4-16u4)
Rewrite t4 as (t2)2.
3t((t2)2-16u4)
Rewrite 16u4 as (4u2)2.
3t((t2)2-(4u2)2)
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=t2 and b=4u2.
3t((t2+4u2)(t2-(4u2)))
Factor.
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Simplify.
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Remove parentheses.
3t((t2+4u2)(t2-1⋅4u2))
Rewrite 4u2 as (2u)2.
3t((t2+4u2)(t2-(2u)2))
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=t and b=2u.
3t((t2+4u2)((t+2u)(t-(2u))))
Factor.
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Multiply 2 by -1.
3t((t2+4u2)((t+2u)(t-2u)))
Remove unnecessary parentheses.
3t((t2+4u2)(t+2u)(t-2u))
3t((t2+4u2)(t+2u)(t-2u))
3t((t2+4u2)(t+2u)(t-2u))
Remove unnecessary parentheses.
3t(t2+4u2)(t+2u)(t-2u)
3t(t2+4u2)(t+2u)(t-2u)
Factor 3t^5-48tu^4

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