6 w 4 − 54 w 2 = 6 w 2 ( w 2 − 9 ) = 6 w 2 ( w 2 − 3 2 ) = 6 w 2 ( w − 3 ) ( w + 3 )
6 w 4 − 54 w 2 = 6 w 2 ⋅ w 2 − 6 w 2 ⋅ 9 = 6 w 2 ⋅ ( w 2 − 9 ) = 6 w 2 ( w − 3 ) ( w + 3 )
The expression 6 w 4 − 54 w 2 can be factored as 6 w 2 ( w − 3 ) ( w + 3 ) . First, we factor out the common term 6 w 2 and then recognize that w 2 − 9 is a difference of squares. The final factorization is complete and includes all possible factors.
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