Rút gọn biểu thức sau:
a, 5(2x – 1) ² + 4 ( x- 1) (x +3 ) – 2( 5- 3x) ²
b, (9x – 1) ² + (1 -5x ) ² + 2 (9x -1 ) ( 1-5x )
c, ( x ² – 5x + 1) ² + 2( 5x – 1) ( x ² – 5x + 1) + (5x- 1)
d, ( x ² + 3x + 1) ² + ( 3x – 1) ² – 2( x ² + 3x + 1) (3x -1 )
e, ( x + y ) ³ – ( x – y ) ³
$a)5(2x-1)^{2}+4 ( x- 1) (x +3 ) – 2( 5- 3x)^{2}$
$⇔5((2x)^{2}-2.2x.1+1^{2})+4(x^{2}+3x-x-3)-2(5^{2}-2.5.3x+(3x)^{2})$
$⇔5(4x^{2}-4x+1)+4x^{2}+12x-4x-12-2(25-30x+9x^{2})$
$⇔20x^{2}-20x+5+4x^{2}+12x-4x-12- 50+60x-18x^{2}$
$⇔6x^{2}+48x-57$
$b)(9x-1)^{2}+(1-5x)^{2}+2(9x-1)(1-5x)$
$⇔(9x-1-1-5x)(9x-1+1+5x)+2(9x-45x^{2}-1+5x)$
$⇔56x-24x+18x-50x^{2}-2+10x$
$⇔60x-2$
$c) ( x ^{2} – 5x + 1) ^{2} + 2( 5x – 1) ( x ^{2} – 5x + 1) + (5x- 1)$
$=( x^{2} – 5x + 1)^{2}+( 5x – 1) ( x^{2} – 5x + 1) +( 5x – 1) ( x^{2} – 5x + 1) + (5x- 1)$
$=(x^{2} – 5x + 1)( x^{2}- 5x + 1+5x-1)+( 5x – 1)(x^{2} – 5x + 2)$
$=(x ² – 5x + 1)x ² +( 5x – 1)(x ² – 5x + 2)$
$=(x ^{2}- 5x + 1)x^{2}+(x^{2} – 5x + 1)5x+5x-x^{2} +5x -1-1$
$=x^{4} -5x^{3} +x^{2} +5x^{3} -25x^{2}+5x -x ²+10x-2$
$=x^{4} -25x^{2} +15x-2^{}$