Đáp án: $a)(a+b+c)(ab+bc+ac)$
$b)6(x^2-4x+1)(x-1)^2$
$c)(6x-3y-4)(2x-y-2)$
Giải thích các bước giải:
$a)a(b^2+c^2+bc)+b(a^2+c^2+ac)+c(b^2+a^2+ab)$
$=ab^2+ac^2+abc+a^2b+bc^2+abc+b^2c+a^2c+abc$
$=(a^2b+ab^2+abc)+(a^2c+abc+ac^2)+(abc+b^2c+bc^2)$
$=ab(a+b+c)+ac(a+b+c)+bc(a+b+c)$
$=(a+b+c)(ab+bc+ac)$
$b)2(x^2-6x+1)^2+5(x^2-6x+1)(x^2+1)+2(x^2+1)^2$
$=2(x^2-6x+1)^2+(x^2-6x+1)(x^2+1)+4(x^2-6x+1)(x^2+1)+2(x^2+1)^2$
$=(x^2-6x+1)[2(x^2-6x+1)+(x^2+1)]+2(x^2+1)[2(x^2-6x+1)+(x^2+1)]$
$=[2(x^2-6x+1)+(x^2+1)][(x^2-6x+1)+2(x^2+1)]$
$=(2x^2-12x+2+x^2+1)(x^2-6x+1+2x^2+2)$
$=(3x^2-12x+3)(3x^2-6x+3)$
$=3(x^2-4x+1).3(x^2-2x+1)$
$=6(x^2-4x+1)(x-1)^2$
$c)12x^2-20x-12xy+10y+8+3y^2$
$=12x^2-6xy-8x-6xy+3y^2+4y-12x+6y+8$
$=(12x^2-6xy-8x)-(6xy-3y^2-4y)-(12x-6y-8)$
$=2x(6x-3y-4)-y(6x-3y-4)-2(6x-3y-4)$
$=(6x-3y-4)(2x-y-2)$
