Factor each expression completely.

U se : a 2 − b 2 = ( a − b ) ( a + b ) ( a ± b ) 2 = ( a 2 ± 2 ab + b 2 ============================== 27. 18 z 2 − 8 = 2 ( 9 z 2 − 4 ) = 2 [ ( 3 z ) 2 − 2 2 ] = 2 ( 3 z − 2 ) ( 3 z + 2 ) 29. 2 a 2 − 16 a + 32 = 2 ( a 2 − 8 a + 16 ) = 2 ( a 2 − 2 a ⋅ 4 + 4 2 ) = 2 ( a − 4 ) 2 = 2 ( a − 4 ) ( a − 4 ) 31. 12 x 2 + 36 x + 27 = 3 ( 4 x 2 + 12 x + 9 ) = 3 [( 2 x ) 2 + 2 ⋅ 2 x ⋅ 3 + 3 2 ] = 3 ( 2 x + 3 ) 2 = 3 ( 2 x + 3 ) ( 2 x + 3 )
33. 3 x 2 − 24 x − 27 = 3 ( x 2 − 8 x − 9 ) = 3 ( x 2 + x − 9 x − 9 ) = 3 [ x ( x + 1 ) − 9 ( x + 1 )] = 3 ( x + 1 ) ( x − 9 ) 35. − x 2 + 5 x − 4 = − ( x 2 − 5 x + 4 ) = − ( x 2 − x − 4 x + 4 ) = − [ x ( x − 1 ) − 4 ( x − 1 )] = − ( x − 1 ) ( x − 4 ) 37. x 2 − y 2 = ( x − y ) ( x + y ) 39. − 6 z 2 − 600 = − 6 ( z 2 + 100 )

Answered by Anonymous | 2024-06-10

To factor expressions completely, one can identify the greatest common factor and look for patterns such as the difference of squares or perfect squares. For example, 18 z 2 − 8 factors to 2 ( 3 z − 2 ) ( 3 z + 2 ) , while 2 a 2 − 16 a + 32 factors to 2 ( a − 4 ) 2 . Each expression can be simplified using basic algebraic identities.
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Answered by Anonymous | 2024-09-30