Math, asked by ashadsheikh2053, 9 months ago

Factorise 4a2 -16b2 +64c2 -32ac

Answers

Answered by mysticd

1

4a² - 16b² + 64c² - 32ac

= 4a² + 64c² - 32ac - 16b²

= [ (2a)² + (8c)² - 2×(2a)×(8c) ] - (4b)²

= ( 2a - 8c )² - (4b)²

= [ (2a-8c) + 4b ] [ (2a-8c) - 4b ]

= ( 2a - 8c + 4b )( 2a - 8c - 4b )

= 2( a - 4c + 2b ) × 2( a - 4c - 2b )

= 4( a - 4c + 2b )( a - 4c - 2b )

Therefore.,

4a² - 16b² + 64c² - 32ac

= 4( a - 4c + 2b )( a - 4c - 2b )

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