Question

Factorise each of the following: (3x – 4y)⁴ – x⁴ using identites proper way​

Answer 1

${(3x - 4y)}^{4} - {x}^{4}$

$= { ({(3x - 4y)}^{2}) }^{2} - ({x}^{2})^{2}$

$= ((3x - 4y)^{2} - {x}^{2} )((3x - 4y)^{2} + {x}^{2} ))$

$= (3x - 4y + x)(3x - 4y - x)(9 {x}^{2} + 16 {y}^{2} - 24xy + {x}^{2} )$

$= (4x - 4y)(2x - 4y)(10 {x}^{2} + 16 {y}^{2} - 24xy)$

$= 8(x - y)(x - 2y) \times 2 \times (5 {x}^{2} + 8 {y}^{2} - 12xy)$

$= 16(x - y)(x - 2y)(5 {x}^{2} + 8 {y}^{2} - 12xy)$