Question

find lcm of a^8-b^8 and (a^4-b^4)(a+b)​

Answer 1

Answer:

$( {a}^{8} - {b}^{8} )(a + b) \\ [OR] \\ {a}^{9} + {a}^{8} b - ab ^{8} - {b}^{9}$

Step-by-step explanation:

${a}^{8} - {b}^{8} = \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ( {a}^{4} + {b}^{4} )( {a}^{2} + {b}^{2} )(a + b)(a - b) \\ ( {a}^{4} - b ^{4} )(a + b) = ( {a}^{2} + {b}^{2} )(a + b)(a - b)(a + b)$

Common factors of both polynomials are:-

(a² + b²) ,

(a + b), and

(a - b)

So, taking these once, we multiply them with the rest of the factors of both polynomials (just the same we do with numbers!).

$LCM = ( {a}^{2} + {b}^{2} )(a + b)(a - b)( {a}^{4} + {b}^{4} )(a + b) \\ \\ = ( {a}^{2} + b^{2} )( {a}^{2} - {b}^{2} )( {a}^{4} + {b}^{4} )(a + b) \\ = ( {a}^{4} - {b}^{4} )( {a}^{4} + {b}^{4} )(a + b) \\ = ( {a}^{8} - {b}^{8} )(a + b) \\ = {a}^{9} + {a}^{8} b - ab ^{8} - {b}^{9}$

So, there! You got your answer!

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