Question

Resolve into factors x⁴-(x+y)⁴​

Answer 1

Answer:

by using ,

${a}^{2} - {b}^{2} = (a + b)(a - b)$

Also,

$(a + b) {}^{2} = a {}^{2} + b {}^{2} + 2ab$

we have,

${ ({x}^{2} })^{2} - {( {(x + y)}^{2} })^{2} \\ = ( {x}^{2} + (x + y) {}^{2} ) \times ( {x}^{2} - (x + y) {}^{2} ) \\ =( x {}^{2} + {x}^{2} + y {}^{2} + 2xy) \times ( {x}^{2} - {x}^{2} - y {}^{2} - 2xy) \\ = (2 {x}^{2} + {y}^{2} + 2xy) \times ( - {y}^{2} - 2xy)$