Question

factorise 81x^4-256y^4

Answer 1

Answer:

( 9 x² + 16 y² )( 3 x + 4 y )( 3 x - 4 y )

Step-by-step explanation:

81 x⁴ - 256 y⁴

==> ( 9 x² )² - ( 16 y² )² [ Using a² - b² = ( a + b )( a - b ) ]

==> ( 9 x² + 16 y² )( 9 x² - 16 y² )

==> ( 9 x² + 16 y² ) [ ( 3 x )² - ( 4 y )² ]

==> ( 9 x² + 16 y² )( 3 x + 4 y )( 3 x - 4 y )

[ Using a² - b² = ( a + b )( a - b ) ]

==> ( 9 x² + 16 y² )( 3 x + 4 y )( 3 x - 4 y )

Hope it helps ya:)

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Answer 2

Hi.

$81x^4 - 256y^4\\\\= (9x)^4 - (16y)^4\\\\= ((9x)^2)^2 - ((16y)^2)^2\\\\Using \: \: a^2 - b^2 = (a+b)(a-b)\\\\((9x)^2 + (16y)^2)((9x^2) - (16y)^2)\\\\Again \: Using \: \: a^2 - b^2 = (a+b)(a-b)\\\\\boxed{(81x^2 + 256x^2)(9x+16y)(9x-16y)}$

Hope it helps.