11) Ta có: \(a^6+a^4+a^2b^2+b^4-b^6\)

\(=a^6-b^6+a^4+a^2b^2+b^4\)

\(=\left(a^2-b^2\right)\left(a^4+a^2b^2+b^4\right)+\left(a^4+a^2b^2+b^4\right)\)

\(=\left(a^4+a^2b^2+b^4\right)\left(a^2-b^2+1\right)\)

12) Ta có: \(x^3+3xy+y^3-1\)

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

\(=\left[\left(x+y\right)^3-1\right]-3xy\left(x+y-1\right)\)

\(=\left(x+y-1\right)\left[x^2+2xy+y^2+x+y+1\right]-3xy\left(x+y-1\right)\)

\(=\left(x+y-1\right)\left(x^2-xy+y^2+x+y+1\right)\)

14) Ta có: \(x^8+x+1\)

\(=x^8+x^7-x^7-x^6+x^6+x^5-x^5-x^4+x^4+x^3-x^3+x^2-x^2+x+1\)

\(=x^6\left(x^2+x+1\right)-x^5\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)

15) Ta có: \(x^8+3x^4+4\)

\(=x^8+4x^4+4-x^4\)

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

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

\(3x^2+22xy+11x+37y+7y^2+10\)

\(=3x^2+xy+21xy+5x+6x+2y+35y+7y^2+10\)

\(=\left(3x^2+xy+5x\right)+\left(21xy+7y^2+35y\right)+\left(6x+2y+10\right)\)

\(=x\left(3x+y+5\right)+7y\left(3x+y+5\right)+2\left(3x+y+5\right)\)

\(=\left(3x+y+5\right)\left(x+7y+2\right)\)

\(=\left(3x+y+5\right)\left(x+7y+2\right)\)

ai giải thích chi tiết hơn con này hộ mình được k ạ :))

\(=3x^2+21xy+xy+6x+5x+2y+35y+7y^2+10\)

\(=\left(3x^2+21xy+6x\right)+\left(xy+7y^2+2y\right)+\left(5x+35y+10\right)\)

\(=3x\left(x+7y+2\right)+y\left(x+7y+2\right)+5\left(x+7y+2\right)=\left(3x+y+5\right)\left(x+7y+2\right)\)

Bài làm 

3x2 – 8x + 4 = (4x2 – 8x + 4) - x2 = (2x – 2)2 – x2 = (2x – 2 + x)(2x – 2 – x) 
= (x – 2)(3x – 2)

a: Ta có: \(-\left(-3x^2\right)^3+4x-9-27x^6\)

\(=27x^6-27x^6+4x-9\)

=4x-9

=-1

3x^2-22xy-4x+8y+7y^2+1 = (y - 3x + 1) (7y - x + 1)