a) \(x^2-25+y^2+2xy=\left(x-y\right)^2-5^2\)
= \(\left(x-y-5\right)\left(x-y+5\right)\)
b) \(x^2-2x-4y^2-4y\)
= \(\left(x^2-2x+1\right)-\left(4y^2+4y+1\right)\)
= \(\left(x-1\right)^2-\left(2y+1\right)^2\)
= \(\left(x-1-2y-1\right)\left(x-1+2y+1\right)\)
= \(\left(x-2y-2\right)\left(x+2y\right)\)
c) Câu này chắc là sai đề nên sửa luôn:
\(16x^3+0,25y^3z^3\)
= \(0,25\left(64x^3+y^3z^3\right)\)
= \(0,25\left(4x+yz\right)\left(16x^2-4xyz+y^2z^2\right)\)
d) \(x^3-x^2-x+1\)
= \(x^2\left(x-1\right)-\left(x-1\right)=\left(x-1\right)^2\left(x+1\right)\)
e) \(x^4+x^3+x^2-1\)
= \(x^3\left(x+1\right)+\left(x+1\right)\left(x-1\right)\)
= \(\left(x+1\right)\left(x^3+x-1\right)\)
f) \(x^4+6x^2y+9y^2-1\)
= \(\left(x^2+3y-1\right)\left(x^2+3y+1\right)\)
g) \(x^2+4x-y^2+4\)
= \(\left(x^2+4x+4\right)-\left(y^2-4y+4\right)\)
= \(\left(x+2\right)^2-\left(y-2\right)^2\)
= \(\left(x+2-y+2\right)\left(x+2+y-2\right)\)
= \(\left(x-y+4\right)\left(x+y\right)\)
h) \(x^3+3x^2-3x-1\)
= \(x^3-x^2+4x^2-4x+x-1\)
= \(x^2\left(x-1\right)+4x\left(x-1\right)+\left(x-1\right)\)
= \(\left(x-1\right)\left(x^2+4x+1\right)\)
\(a,x^2-25+y^2+2xy=\left(x^2+2xy+y^2\right)-25=\left(x+y\right)^2-5^2=\left(x+y+5\right)\left(x+y-5\right)\)\(b,x^2-2x-4y^2-4y=\left(x^2-2x+1\right)-\left(4y^2-4y+1\right)=\left(x-1\right)^2-\left(2y-1\right)^2=\left(x-1-2y+1\right)\left(x-1+2y-1\right)=\left(x-2y\right)\left(x+2y-2\right)\)\(c,16x^3+0,25yz^3=0,25\left(64x^3+yz^3\right)\)
\(d,x^3-x^2-x+1=x^2\left(x-1\right)-\left(x-1\right)=\left(x^2-1\right)\left(x-1\right)=\left(x-1\right)^2\left(x+1\right)\)\(e,x^4+x^3+x^2-1=x^3\left(x+1\right)+\left(x-1\right)\left(x+1\right)=\left(x+1\right)\left(x^3+x-1\right)\)\(f,x^4+6x^2y+9y^2-1=\left(x^2+3y\right)^2-1=\left(x^2+3y+1\right)\left(x^2+3y-1\right)\)\(g,x^2-4x+y^2+4=\left(x-2\right)^2-y^2=\left(x-2-y\right)\left(x-2+y\right)\)\(h,x^3+3x^2-3x-1=x^3-1+3x\left(x-1\right)=\left(x-1\right)\left(x^2+x+1\right)+3x\left(x-1\right)=\left(x-1\right)\left(x^2+4x+1\right)\)
