Question

factorize 16x^4 - (x-3)^4​

Answer 1

Answer:

$16 {x}^{4} - {(x - 3)}^{4} \\ = (4 {x}^{2} ) {}^{2} -( (x - 3) {}^{2} ) {}^{2} \\ = (4 {x}^{2} - (x - 3) {}^{2} )(4 {x}^{2} + (x - 3) {}^{2} ) \\ = ((2x ){}^{2} - (x - 3) {}^{2} )(4 {x}^{2} + {x}^{2} - 6x + 9) \\ =( 2 {x}^{} - x + 3)(2x + x - 3)(5 {x}^{2} - 6x + 9) \\ = (x + 3)(3x - 3)(5 {x}^{2} - 6x + 9) \\ = 3(x + 3)(x - 1)(5 {x}^{2} - 6x + 9)$