Question

Factories: (2x-y)⁶-(2x+y)⁶​

Answer 1

Answer:

(2x+y)

3

+(2x−y)

3

⇒ [(2x)

2

]

3

−[(y)

2

]

3

[ Since, (a+b)(a−b)=a

2

−b

2

]

⇒ [4x

2

]

3

−[y

2

]

3

⇒ 64x

6

−y

6

∴ (2x+y)

3

+(2x−y)

3

=64x

6

−y

6

Answer 2

$\huge\mathfrak\red{Question:}$

Factorise (2x-y)⁶-(2x+y)⁶

$\huge\mathfrak\red{Answer:}$

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

STEP2:

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)

$\huge{\boxed{\tt{Thanks}}}$