Question

5. FACTORISE THE FOLLOWING:256x8 – Y8​

Answer 1

Step-by-step explanation:

We know that,

$\large{ \sf{ \pink{a² - b² = (a+b)(a-b)}}}$

$\sf \pink{{256} {x}^{8} - {y}^{8} }\\ \sf = (16 { {x}^{4} )}^{2} - {({y}^{4} })^{2} \\ \sf= (16 {x}^{4} + {y}^{4} )(16 {x}^{4} - {y}^{4}) \\ \sf = (16 {x}^{4} + {y}^{4}) \{ {(4 {x}^{2} )}^{2} - ({ {y}^{2} )}^{2} \} \\ \sf = (16 {x}^{4} + {y}^{4})(4 {x}^{2} + {y}^{2} )(4 {x}^{2} - {y}^{2} ) \\ \sf = (16 {x}^{4} + {y}^{4})(4 {x}^{2} + {y}^{2} ) \{ {(2x)}^{2} - ({y)}^{2} \} \\\sf = \pink{(16 {x}^{4} + {y}^{4})(4 {x}^{2} + {y}^{2} )(2x + y)(2x - y)}$