Question

[Nguyễn Hoài Thương]

phân tích

(a+b)^3-c^3

x^4+x^3-x^2+x-2

(x^2+8x+7)*(x^2+8x+15)+15

x^7+x^2+1

xy(x+y)+yz(y+z)+zx(z+x)+yxz

Answer 1

[@Nk>↑@]

(*)\(\left(x^2+8x+7\right)\left(x^2+8x+15\right)+15\)

\(=y\left(y+8\right)+15\) tại \(y=x^2+8x+7\)

\(=y^2+8y+15\)

\(=y^2+3y+5y+15\)

\(=y\left(y+3\right)+5\left(y+3\right)\)

\(=\left(y+5\right)\left(y+3\right)\)

(*)\(x^7+x^2+1\)

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

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

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

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

Answer 2

[@Nk>↑@]

(*)\(\left(a+b\right)^3-c^3=\left(a+b-c\right)\left[\left(a+b\right)^2+\left(a+b\right)c+c^2\right]=\left(a+b-c\right)\left(a^2+2ab+b^2+ac+bc+c^2\right)\)

(*)\(x^4+x^3-x^2+x-2=x^4-x^3+2x^3-2x^2+x^2-x+2x-2\)

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

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

...........................................\(=\left(x-1\right)\left[x\left(x^2+1\right)-2\left(x^2+1\right)\right]\)

............................................

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