Giải thích các bước giải:
Ta có:
a, 5x(x-2)-3$x^{2}$.(x-2)= 5.$x^{2}$ - 10x - 3.$x^{3}$ +6.$x^{2}$
= (-3.$x^{3}$ + 6.$x^{2}$)+ (5.$x^{2}$ - 10x)
= -3.$x^{2}$(x - 2) + 5x( x - 2) = (x-2)(-3$x^{2}$ + 5x)
= (x-2)x(-3x+5)
b, 16$x^{2}$ - $(x^{2}+4)^2$ = 16$x^{2}$ - $x^4$ - 8$x^2$ - $4^2$
= - $x^4$ + 8$x^2$ - 16
= - $x^4$ + 2$x^3$ - 2$x^3$ + 4$x^2$ + 4$x^2$ - 8x + 8x -16
= -$x^3$(x-2) -2$x^2$(x-2)+4x(x-2)+8(x-2)
= (x-2)(-$x^3$ - 2$x^2$ + 4x + 8)
= (x-2)[ (-$x^3$ + 2$x^2$) - (4$x^2$ - 8x) - (4x-8)]
= (x-2)[-$x^2$(x-2) - 4x(x-2) - 4(x-2)]
= (x-2)(x-2)(-$x^2$ -4x-4) = $(x-2)^2$ [-$x^2$ - 2x -2x -4]
= $(x-2)^2$ (x+2)(-x-2)
c, 5$x^2$-5xy+7y-7x = 5x(x-y) + 7(y-x) = (x-y)(5x-7)
d, 3$x^2$-8x+4 = 3$x^2$- 6x - 2x +4 = 3x(x-2) - 2(x-2) = (x-2)(3x-2)
e, $x^4$+64 = $(x^2)^2$ + $8^2$ = $(x^2+8)^2$ - 16$x^2$ = $(x^2+8)^2$ - $(4.x)^2$
= ($x^2$ - 4x+8)($x^2$ + 4x+8)
