1. $a\left(b+c\right)^2+b\left(c+a\right)^2+c\left(a+b\right)^2-4abc$

$=\left(ab+ac\right)\left(b+c\right)+bc^2+2abc+a^2b+a^2c+2abc+b^2c-4abc$

$=\left(ab+ac\right)\left(b+c\right)+\left(bc^2+b^2c\right)+\left(a^2b+a^2c\right)$

$=\left(ab+ac\right)\left(b+c\right)+bc\left(b+c\right)+a^2\left(b+c\right)$

$=\left(ab+ac+bc+a^2\right)\left(b+c\right)$

$=\left[\left(ab+bc\right)+\left(ac+a^2\right)\right]\left(b+c\right)$

$=\left[b\left(a+c\right)+a\left(a+c\right)\right]\left(b+c\right)$

$=\left(a+b\right)\left(a+c\right)\left(b+c\right)$

2. Đặt $x^2+x+1=a$ $\Rightarrow\left(x^2+x+1\right)\left(x^2+x+2\right)-12=a\left(a+1\right)-12$

$=a^2+a-12=\left(a^2-3a\right)+\left(4a-12\right)$

$=a\left(a-3\right)+4\left(a-3\right)=\left(a+4\right)\left(a-3\right)$

$=\left(x^2+x+1+4\right)\left(x^2+x+1-3\right)=\left(x^2+x+5\right)\left(x^2+x-2\right)$

phân tích đa thức thành nhân tử

6xy+5x-5y-3x2-3y2

$6xy+5x-5y-3x^2-3y^2$

$=5\left(x-y\right)-\left(3x^2-6xy+3y^2\right)$

$=5\left(x-y\right)-3\left(x-y\right)^2$

$=5\left(x-y\right)-\left(3x-3y\right)\left(x-y\right)$

$=\left(5-3x+3y\right)\left(x-y\right)$

bài 1 : phân tích các đa thức sau thành nhân tử

a) x3-1/16x

b) (3x + 1 ) 2 -(x+2)2

c) 4xy-x2-4y2+16

d) 3x2+6x-3y2+3

b, $\left(3x+1\right)^2-\left(x+2\right)^2$

$=\left(3x+1-x-2\right)\left(3x+1+x+2\right)$

$=\left(2x-1\right)\left(4x+3\right)$

c, $4xy-x^2-4y^2+16$

$=-\left(x^2-4xy+4y^2-16\right)$

$=-\left[\left(x-2y\right)^2-16\right]$

$=16-\left(x-2y\right)^2$

$=\left(4-x+2y\right)\left(4+x-2y\right)$

phân tích đa thức thành nhân tử: x5+x+1

$x^5+x+1$

$=x^5+x^4-x^4+x^3-x^3+x^2-x^2+x+1$

$=\left(x^5+x^4+x^3\right)-\left(x^4+x^3+x^2\right)+\left(x^2+x+1\right)$

$=$ $x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)$

$=\left(x^2+x+1\right)\left(x^3-x^2+1\right)$

Phân tích đa thức sau thành nhân tử

x4-6x3+12x2-14x+3

$x^4-6x^3+12x^2-14x+3$

$=x^4-2x^3+3x^2-4x^3+8x^2-12x+x^2-2x+3$

$=\left(x^4-4x^3+x^2\right)-\left(2x^3-8x^2+2x\right)$$+\left(3x^2-12x+3\right)$

$=x^2\left(x^2-4x+1\right)-2x\left(x^2-2x+3\right)+3\left(x^2-4x+1\right)$

$=\left(x^2-4x+1\right)\left(x^2-2x+3\right)$