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c) xét giá trị riêng
\(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz\)
\(=xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+xyz+xyz\)
\(=xy\left(x+y\right)+y^2z+yz^2+x^2z+xz^2+xyz+xyz\)
\(=xy\left(x+y\right)+y^2z+xyz+yz^2+xz^2+x^2z+xyz\)
\(=xy\left(x+y\right)+yz\left(x+y\right)+z^2\left(x+y\right)+xz\left(x+y\right)\)
\(=\left(x+y\right)\left(xy+yz+z^2+xz\right)\)
\(=\left(x+y\right)\left[y\left(x+z\right)+z\left(x+z\right)\right]=\left(x+y\right)\left(y+z\right)\left(x+z\right)\)
a) \(x^2-y^2-x-y\)
\(=\left(x+y\right)\left(x-y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-1\right)\)
\(yz\left(y+z\right)+zx\left(z-x\right)-xy\left(x+y\right)\)
\(=yz\left(y+z\right)+zx\left(z-x\right)-xy\left[\left(y+z\right)-\left(z-x\right)\right]\)
\(=yz\left(y+z\right)+zx\left(z-x\right)-xy\left(y+z\right)+xy\left(z-x\right)\)
\(=y\left(y+z\right)\left(z-x\right)+x\left(z-x\right)\left(z-y\right)\)
\(=\left(z-x\right)\left(yz-xy+xz-xy\right)\)
a)\(4x^4+y^4=\left(4x^4+y^4+4x^2y^2\right)-4x^2y^2\)
\(=\left(2x^2+y^2\right)^2-\left(2xy\right)^2\)
\(=\left(2x^2+y^2-2xy\right)\left(2x^2+y^2+2xy\right)\)
b)\(\left(x^2-3x-1\right)^2-12\left(x^2-3x-1\right)+27\)
Đặt x^2 - 3x - 1 = A
\(\Rightarrow A^2-12A+27=\left(A^2-12A+36\right)-9\)
\(=\left(A-6\right)^2-9=\left(A-6-3\right)\left(A-6+3\right)\)
\(=\left(A-9\right)\left(A-3\right)\)
Hay \(=\left(x^2-3x-1-9\right)\left(x^2-3x-1-3\right)\)
\(=\left(x^2-3x-10\right)\left(x^2-3x-4\right)\)
\(=\left(x-5\right)\left(x+2\right)\left(x-4\right)\left(x+1\right)\)
c)\(x^3-x^2-5x+125\)
\(=\left(x^3+5^3\right)-\left(x^2+5x\right)\)
\(=\left(x+5\right)\left(x^2-5x+25\right)-x\left(x+5\right)\)
\(=\left(x+5\right)\left(x^2-5x+25-x\right)\)
\(=\left(x+5\right)\left(x^2-6x+25\right)\)
d)\(xy\left(x+y\right)+yz\left(y+z\right)+zx\left(z+x\right)+2xyz\)
\(=\left(x+y\right)\left(y+z\right)\left(x+z\right)\)
Mình có việc bận nên chỉ đưa được kết quả ý d) thật lòng mong các bạn tự tham khảo và giải
k) \(x^3-x+3x^2+3xt^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left[\left(x+y\right)^2-1\right]\)
\(=\left(x+y\right)\left(x+y+1\right)\left(x+y-1\right)\)
h) \(a^3-a^2x-ay+xy\)
\(=a^2\left(a-x\right)-y\left(a-x\right)\)
\(=\left(a^2-y\right)\left(a-x\right)\)
a) \(x^6-y^6=\left(x^3-y^3\right)\left(x^3+y^3\right)\)
b) \(\left(x+y\right)^2-\left(x-y\right)^2=\left(2y\right)\left(2x\right)\)
c) \(\left(3x+1\right)^2-\left(x+1\right)^2=4x\left(2x+1\right)\)
f) \(x^2-2xy+y^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\)
\(d,x^2-10x+25=\left(x-5\right)^2\)
\(e,x^2-x-y^2-y=x^2-y^2-x-y=\left(x-y\right)\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(x-y-1\right)\)
\(h,xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz\)
\(=xy\left(x+y\right)+yz\left(y+z\right)+xyz+xz\left(x+z\right)+2xyz+xyz\)
\(=xy\left(x+y\right)+yz\left(y+z+x\right)+xz\left(x+z+y\right)\)
\(=xy\left(x+y\right)+z\left(x+y\right)\left(x+y+z\right)\)
\(=\left(x+y\right)\left(xy+zx+zy+z^2\right)\)
\(=\left(x+y\right)\left(x+z\right)\left(y+z\right)\)
\(g,3\left(x-3\right)\left(x+7\right)+\left(x-4\right)^2+48\)
\(=3\left(x^2+4x-21\right)+\left(x^2-8x+16\right)+48\)
\(=3x^2+12x-63+x^2-8x+64\)
\(=4x^2+4x+1=\left(2x+1\right)^2\)
\(j,x^3-x+y^3-y=x^3+y^3-x-y=\left(x+y\right)\left(x^2-xy+y^2\right)-\left(x+y\right)=\left(x+y\right)\left(x^2-xy+y^2-1\right)\)
a) \(5x-5y+ax-ay\)
\(\Leftrightarrow\) \(\left(5x+ax\right)-\left(5y+ay\right)\)
\(\Leftrightarrow\) \(x\left(5+a\right)-y\left(5+a\right)\)
\(\Leftrightarrow\) \(\left(5+a\right)\left(x-y\right)\)
a,\(x^3+2x^2y+xy^2-9x\)
=x(\(x^2+2xy+y^2\)-9)
=x[(\(x^2+2xy+y^2\))-9]
=x[\(\left(x+y\right)^2\)-9]
b,2x-2y-\(x^2+2xy-y^2\)
=(2x-2y)-(\(x^2-2xy+y^2\))
=2(x-y)-\(\left(x-y\right)^2\)
=(x-y)(2-x+y)
c,\(x^4-2x^2\)
=\(x^2\left(x^2-2\right)\)
d,\(x^2-4x+3\)
=\(x^2-4x+4-1\)
=\(\left(x^2-4x+2^2\right)\)-1
=\(\left(x-2\right)^2\)-1
=(x-2-1)(x-2+1)
thông cảm mk chỉ làm đc từng này thôi
à..mà bạn xem lại ý e, cho mk đc k
o: \(x^3-xy^2+x^2y-y^3\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)+xy\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2+2xy+y^2\right)\)
\(=\left(x-y\right)\left(x+y\right)^2\)
p: \(a^3-ma-mb+b^3\)
\(=\left(a+b\right)\left(a^2-ab+b^2\right)-m\left(a+b\right)\)
\(=\left(a+b\right)\left(a^2-ab+b^2-m\right)\)
q: \(\left(3x+1\right)^3-\left(1-2x\right)^3\)
\(=\left(3x+1\right)^3+\left(2x-1\right)^3\)
\(=\left(3x+1+2x-1\right)\left[\left(3x+1\right)^2-\left(3x+1\right)\left(2x-1\right)+\left(2x-1\right)^2\right]\)
\(=5x\left[9x^2+6x+1-6x^2+3x-2x+1+4x^2-4x+1\right]\)
\(=5x\left(7x^2+5x+3\right)\)