Question

Factorise: a⁴-(a-b)⁴​

Answer 1

We have,

$\quad {a}^{4} - {(a - b)}^{4} \\ = {( {a}^{2} )}^{2} - {( {(a - b)}^{2} )}^{2} \\ = ( {a}^{2} - {(a - b)}^{2} )( {a}^{2} + {(a - b)}^{2} ) \\ = (a - (a - b))(a + (a - b))( {a}^{2} + {(a - b)}^{2} ) \\ = ( \cancel{a} - \cancel{a} + b)(a + a - b)( {a}^{2} + {a}^{2} + {b}^{2} + 2ab) \\ = b(2a - b)(2 {a}^{2} + {b}^{2} + 2ab)$

Answer 2

Answer:

$a {}^{4} - (a -b) {}^{4}$

$(a - b) {}^{4} = a {}^{4} - 4a {}^{3 } + 6a {}^{2}b {}^{2} - 4ab {}^{ 3} + b {}^{4}$

then

$a {}^{4} - a {}^{4} + 4a {}^{3}b \: - 6a {}^{2}b {}^{2} + 4ab {}^{3} - b {}^{4}$

please mark me as brainliest