Question

Factorise: 2a⁴ - 32b⁴

Answer 1

Bonjour!

$= > 2 {a}^{4} - 32 {b}^{4} \\ \\ = > 2( {a}^{4} - 16 {b}^{4} ) \\ \\ = >2 ( {a}^{4} - ({2}^{4} )( {b}^{4} )) \\ \\ = > 2( {a}^{4} - {(2b)}^{4} ) \\ \\ = > 2( {a}^{2} - {2b}^{2} )( {a}^{2} + {2b}^{2} ) \\ \\ = > 2(a - 2b)(a + 2b)( {a}^{2} + {2b}^{2} )$

Hope this helps...:)

Answer 2

Hey there!

$= 2 {a}^{4} - 32 {b}^{4} \\ = 2( \: ( { {a}^{2} })^{2} - ( {4b})^{2} )$

= 2 ( a² + 4b² ) ( a² - 4b² )

= 2 ( a² + 4b² ) ( a + 2b ) ( a - 2b )

Used identity = a² - b² = ( a + b ) ( a - b )

Hope helped!