Question

Factorise (2x-y)^6-(2x+y)^6

Answer 1

(2x-y)6-(2x+y)6

Final result :

-8xy • (12x2 + y2) • (4x2 + 3y2)

Step by step solution :

Step 1 :

1.1 Evaluate : (2x-y)6 = 64x6-192x5y+240x4y2-160x3y3+60x2y4-12xy5+y6

1.2 Evaluate : (2x+y)6 = 64x6+192x5y+240x4y2+160x3y3+60x2y4+12xy5+y6

Step 2 :

Pulling out like terms :

2.1 Pull out like factors :

-384x5y - 320x3y3 - 24xy5 = -8xy • (48x4 + 40x2y2 + 3y4)

Trying to factor a multi variable polynomial :

2.2 Factoring 48x4 + 40x2y2 + 3y4

Try to factor this multi-variable trinomial using trial and error

Found a factorization : (12x2 + y2)•(4x2 + 3y2)

Final result :

-8xy • (12x2 + y2) • (4x2 + 3y2)

mark as brainlist answer