Đáp án:
Bài 1:
a) $4x+23$
b) $-x^{4}+13x^{3}+64x-2163$
c) $12xy^{2}-16y^{3}$
Bài 2:
a) $2x(4xy-4y+1)$
b) $(x-3-y)(x-3+y)$
c) $(x-1)(x+4)(x^{2}+3x+6)$
Giải thích các bước giải:
Bài 1:
a) $(x+2)^{2}-(x+3)(x-3)+10$
$=(x^{2}+4x+4)-(x^{2}-9)+10$
$=x^{2}+4x+4-x^{2}+9+10$
$=4x+23$
b) $(x+5)(x^{2}-5x+25)-x(x-4)^{3}+16$
$=(x^{3}+125)-x(x^{3}-3x^{2}.4+3x.16-64)+16$
$=x^{3}+125-x^{4}+12x^{3}-48x^{2}+64x+16$
$=-x^{4}+13x^{3}+64x-2163$
c) $(x-2y)^{3}-(x+2y)(x^{2}-2xy+4y^{2})+6x^{2}y$
$=(x^{3}-3x^{2}.2y+3x.4y^{2}-8y^{3})-(x^{3}+8y^{3})+6x^{2}y$
$=x^{3}-3x^{2}.2y+3x.4y^{2}-8y^{3}-x^{3}-8y^{3}+6x^{2}y$
$=12xy^{2}-16y^{3}$
Bài 2:
a) $8x^{2}y-8xy+2x$
$=2x(4xy-4y+1)$
b) $x^{2}-6x-y^{2}+9$
$=(x^{2}-6x+9)-y^{2}$
$=(x-3)^{2}-y^{2}$
$=(x-3-y)(x-3+y)$
c) $(x^{2}+2x)(x^{2}+4x+3)-24$
$=x^{4}+4x^{3}+3x^{2}+2x^{3}+8x^{2}+6x-24$
$=x^{4}+6x^{3}+11x^{2}-18x+24x-24$
$=x^{4}-x^{3}+7x^{3}-7x^{2}+18x^{2}-18x+24x-24$
$=x^{3}(x-1)+7x^{2}(x-1)+18x(x-1)+24(x-1)$
$=(x-1)(x^{3}+7x^{2}+18x+24)$
$=(x-1)(x^{3}+4x^{2}+3x^{2}+12x+6x+24)$
$=(x-1)[x^{2}(x+4)+3x(x+4)+6(x+4)]$
$=(x-1)(x+4)(x^{2}+3x+6)$
