Factorization
( x - y )2 - 3(y – x)3
= ( x - y )2 - 3(– x + y)3
Applying exponent rule : ab+c = abac :
( x - y )2 - 3(– x + y)2(– x + y)
Applying formula : (a)2 = (-a)2 :
( x - y )2 - X(x - y)2(– x + y)
Factor out XXXXXX XXXX ( x - y )X :
( x - y )2 [X -3(– x + y)]
= ( x - y )2(1 + 3x - XX)
So,( x - y )2 - X(y – x)3= ( x - y )2(X + 3x - XX)
XXXX(XX-x) – 2xX(x-XX)X
Applying exponent rule : ab+c = abac and XXXXXXX (-a) = -a :
-XXX2(x -XX) – XX2(x-XX) (x -3y)
XXXXXX out common term -XX( x - 3y ) :
-2x( x - 3y ) [ XX2 + 2x(x – XX)]
= -XX( x - 3y )(2yX + XX2 – XXX)
XX, XXX2(XX-x) – 2xX(x-3y)2 =-XX( x - XX )(XX2 + 2x2 – 6xy)
(x-y)2 + X(y-x)3
= ( x - y )X + (– x + y)X
XXXXXXXX exponent XXXX : ab+c = abac :
( x - y )2 + X(– x + y)X(– x + y)
Applying XXXXXXX : (a)X = (-a)2 :
( x - y )2 + X(x - y)X(– x + y)
Factor out XXXXXX term ( x - y )2 :
( x - y )X [1 + 3(– x + y)]
= ( x - y )X(X - 3x + XX)
XX,( x - y )2 + X(y – x)X= ( x - y )2(X - 3x + 3y)
( x - y )X + 2(y – x)
Applying XXXXXXXX XXXX : ab+c = abac XXX XXXXXXX (-a) = -(a) :
( x - y )( x - y ) - 2( x - y )
Factor out common term ( x - y ) :
( x - y )( x - y – 2)
XXXX, ( x - y )2 + 2(y – x) = ( x - y )( x - y – 2)
6x(a+b) – a – b
Since -(a+b) = -a –b :
6x(a+b) – a – b
XX(a+b) – (a + b)
Factor out common term ( a+b ) :
(a+b)(6x – 1)
XXXXX, XX(a+b) – a – b =(a+b)(6x – 1)
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