\(A=2x^2+10x+8\)
\(=2x^2+2x+8x+8\)
\(=2x\left(x+1\right)+8\left(x+1\right)\)
\(=\left(x+1\right)\left(2x+8\right)\)
\(=2\left(x+1\right)\left(x+4\right)\)
\(B=x^2-7xy+10y^2\)
\(=x^2-2xy-5xy+10y^2\)
\(=x\left(x-2y\right)-5y\left(x-2y\right)\)
\(=\left(x-2y\right)\left(x-5y\right)\)
\(C=5x^2+6xy+y^2\)
\(=5x^2+5xy+xy+y^2\)
\(=5x\left(x+y\right)+y\left(x+y\right)\)
\(=\left(x+y\right)\left(5x+y\right)\)
\(D=x^3+8\)
\(=\left(x+2\right)\left(x^2-2x+4\right)\)
\(E=x^4+64\)
\(=[\left(x^2\right)^2+2.x^2.8+64]-16x^2\)
\(=\left(x^2+8\right)^2-\left(4x\right)^2\)
\(=\left(x^2-4x+8\right)\left(x^2+4x+8\right)\)
\(F=x^6+27\)
\(=\left(x^2\right)^3+3^3\)
\(=\left(x^2+3\right)\left(x^4-3x^2+9\right)\)
\(=\left(x^2+3\right)\left[\left(x^4+6x^2+9\right)-9x^2\right]\)
\(=\left(x^2+3\right)\left[\left(x^2+3\right)^2-\left(3x\right)^2\right]\)
\(=\left(x^2+3\right)\left(x^2+3x+3\right)\left(x^2-3x+3\right)\)
\(G=x^4-2x^3+2x-1\)
\(=x^4-x^3-x^3+x^2-x^2+x+x-1\)
\(=x^3\left(x-1\right)-x^2\left(x-1\right)-x\left(x-1\right)+\left(x-1\right)\)
\(=\left(x-1\right)\left(x^3-x^2-x+1\right)\)
\(=\left(x-1\right)\left[x^2\left(x-1\right)-\left(x-1\right)\right]\)
\(=\left(x-1\right)^2\left(x^2-1\right)\)
\(=\left(x-1\right)^3\left(x+1\right)\)
\(H=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-24\)
Đặt \(x^2+5x+5=a\)
\(\Rightarrow H=\left(a-1\right)\left(a+1\right)-24\)
\(=a^2-1-24\)
\(=a^2-25\)
\(=\left(a-5\right)\left(a+5\right)\)
\(=\left(x^2+5x+5-5\right)\left(x^2+5x+5+5\right)\)
\(=\left(x^2+5\right)\left(x^2+5x+10\right)\)
A= \(2x^2\)+8x+2x+8
A= 2x(x+1)+8(x+1)
A= (x+1)(2x+8)
B=\(x^2\)-2xy-5xy+10\(y^2\)
B=x(x-2y)-5y(x-2y)
B=(x-2y)(x-5y)
C= 5\(x^2\)+5xy+xy+\(y^2\)
C= 5x(x+y)+y(x+y)
C= (x+y)(5x+y)
D= \(x^3\)+\(2^3\)
D= (x+2)(\(x^2\)-2x+4)
E= \(\left(x^2\right)^2\)+\(8^2\)
E=-\(\left[\left(x^2\right)^2-8^2\right]\)
E=-\(\left[\left(x^2+8\right)\left(x^2-8\right)\right]\)
F= \(\left(x^2\right)^3\)+\(3^3\)
F= (\(x^2\)+3)(\(x^4\)-3\(x^2\)+9)
G= \(\left(x^2-1\right)\left(x^2+1\right)-2x\left(x^2-1\right)\)
G= (x-1)(x+1)(\(x^2\)+1)-2x(x-1(x+1)
G= (x-1)(x+1)(\(x^2\)+1-2x)
G= (x-1)(x+1)\(\left(x-1\right)^2\)
G= \(\left(x-1\right)^3\)(x+1)
H= (\(x^2\)+5x+5-1)(\(x^2\)+5x+5+1)-24
H= \(\left(x^2+5x+5\right)^2\)-1-24
H= \(\left(x^2+5x+5\right)^2\)-25
H= (\(\left(x^2+5x+5\right)\)+5)(\(\left(x^2+5x+5\right)\)-5)
H= (\(x^2\)+5x+10)(\(x^2\)+5x)
