Question

factorise : 6561a^8 - 256b^8 ​

Answer 1

Answer

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We have ,

• 6561a^8 - 256b^8

= (81^4)^2 - (16b^4)^2)

= (81a^4 + 16b^4) (81a^4 - 16b^4)

= (81a^4 + 16b^4 ) {(9a^2)^2 - (4b^2)^2}

= (81a^4+16b^4){(9a^2 +4b^2)(9a^2-4b^2)}

=(81a^4 +16b^4)(9a^2+4b^2){(3a^2)-(2b^2)}

=(81a^4+16b^4)(9a^2+4b^2){(3a+2b)(3a-2b)}

Additional information

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(a+b)^3=a^3+b^3+3ab(a+b)

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(a+b)^2 = a^2 + b^2 +2ab

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(a-b)^2 = a^2 + b^2 -2ab

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(a-b)(a+b) = a^2 - b^2

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