Question

Factorise 16x⁴-81y⁴​

Answer 1

Answer:

$16 {x}^{4} - 81 {y}^{4} \\ = ({2x})^{4} - ( {3y})^{4} \\ = ({4 {x}^{2} })^{2} - ({9 {y}^{2} })^{2} \\ = (4 {x}^{2} - 9 {y}^{2} )(4 {x}^{2} + 9 {y}^{2} )$

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Answer 2

(4x²+9y²)(2x+3y)(2x-3y)

Step-by-step explanation:

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We know the algebraic identity:

a² - b² = ( a + b )( a - b )

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16x⁴ - 81y⁴

= ( 4x² )² - ( 9y² )²

= ( 4x² + 9y² )( 4x² - 9y² )

= (4x² + 9y²)[ (2x)² - (3y)² ]

= (4x²+9y²)(2x+3y)(2x-3y)