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\(yz\left(y+z\right)+zx\left(z-x\right)-xy\left(x+y\right)\)
\(=yz\left(y+z\right)+zx\left(z-x\right)-xy\left[\left(y+z\right)-\left(z-x\right)\right]\)
\(=yz\left(y+z\right)+zx\left(z-x\right)-xy\left(y+z\right)+xy\left(z-x\right)\)
\(=y\left(y+z\right)\left(z-x\right)+x\left(z-x\right)\left(z-y\right)\)
\(=\left(z-x\right)\left(yz-xy+xz-xy\right)\)
a) \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz\)
\(=x^2y+xy^2+xyz+x^2z+xz^2+xyz+y^2z+yz^2\)
\(=xy\left(x+y+z\right)+xz\left(x+z+y\right)+yz\left(y+z\right)\)
\(=\left(x+y+z\right)\left(xy+xz\right)+yz\left(y+z\right)\)
\(=x\left(x+y+z\right)\left(y+z\right)+yz\left(y+z\right)\)
\(=\left(y+z\right)\left(x^2+xy+xz+yz\right)\)
\(=\left(y+z\right)\left[x\left(x+y\right)+z\left(x+y\right)\right]=\left(y+z\right)\left(x+y\right)\left(x+z\right)\)
b) \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)
\(=\left(x^2y+xy^2+xyz\right)+\left(x^2z+xz^2+xyz\right)+\left(y^2z+yz^2+xyz\right)\)
\(=xy\left(x+y+z\right)+xz\left(x+z+y\right)+yz\left(y+z+x\right)\)
\(=\left(x+y+z\right)\left(xy+xz+yz\right)\)
P/s: Sai sót xin bỏ qua.
tuổi con HN là :
50 : ( 1 + 4 ) = 10 ( tuổi )
tuổi bố HN là :
50 - 10 = 40 ( tuổi )
hiệu của hai bố con ko thay đổi nên hiệu vẫn là 30 tuổi
ta có sơ đồ : bố : |----|----|----|
con : |----| hiệu 30 tuổi
tuổi con khi đó là :
30 : ( 3 - 1 ) = 15 ( tuổi )
số năm mà bố gấp 3 tuổi con là :
15 - 10 = 5 ( năm )
ĐS : 5 năm
mình nha
a) \(2\left(x-y\right)+x^2-y^2\\ =2\left(x-y\right)+\left(x^2-y^2\right)\\ =2\left(x-y\right)+\left(x+y\right)\left(x-y\right)\\ =\left(x-y\right)\left(2+x-y\right)\)
b) \(x^3-4x^2-9x+36\\ =x^2\cdot x-4x^2-9x+36\\ =x^2\left(x-4\right)-9\left(x-4\right)\\=\left(x-4\right)\left(x^2-9\right)\\ =\left(x-4\right)\left(x-3\right)\left(x+3\right)\)
c) \(2x^2+2y^2-x^2z+2-y^2z-2\\ =2\left(x^2+y^2\right)-z\left(x^2+y^2\right)+\left(2-2\right)\\ =\left(x^2+y^2\right)\left(2-z\right)\)
d) \(x^3+y^3+2x^2-2xy+2y^2\\ =\left(x+y\right)\left(x^2-xy+y^2\right)+2\left(x^2-xy+y^2\right)\\ =\left(x^2-xy+y^2\right)\left(x+y+2\right)\)
e) \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz\\ =x^2y+xy^2+xyz+x^2z+xz^2+xyz+y^2z+yz^2\\ =xy\left(x+y+z\right)+xz\left(x+y+z\right)+yz\left(y+z\right)\\ =\left(y+z\right)\left(x^2+xy+xz+yz\right)\\ =\left(y+z\right)\left(z+x\right)\left(x+y\right)\)
b \(x^8y^8+x^4y^4+1=x^8y^8+2x^4y^4+1-x^4y^4=\left(x^4y^4\right)^2+2x^4y^4+1-\left(x^2y^2\right)^2\)
\(=\left(x^4y^4+1\right)^2-\left(x^2y^2\right)^2=\left(x^4y^4-x^2y^2+1\right)\left(x^4y^4+x^2y^2+1\right)\)
c \(x^2y+xy^2+xz^2+x^2z+y^2z+yz^2+2xyz=\left(x^2y+x^2z+xyz+xy^2\right)+\left(xz^2+yz^2+xyz+y^2z\right)\)
\(=x\left(xy+xz+yz+y^2\right)+z\left(xz+yz+xy+y^2\right)=\left(x+z\right)\left(xy+xz+yz+y^2\right)\)
\(=\left(x+z\right)\left(x\left(y+z\right)+y\left(y+z\right)\right)=\left(x+z\right)\left(x+y\right)\left(y+z\right)\)
a \(3xyz+x\left(y^2+z^2\right)+y\left(x^2+z^2\right)+z\left(x^2+y^2\right)=3xyz+xy^2+xz^2+x^2y+yz^2+x^2z+y^2z\)
\(=\left(x^2y+x^2z+xyz\right)+\left(xy^2+xyz+y^2z\right)+\left(xyz+xz^2+yz^2\right)\)
\(=x\left(xy+xz+yz\right)+y\left(xy+xz+yz\right)+z\left(xy+xz+yz\right)=\left(x+y+z\right)\left(xy+xz+yz\right)\)
\(a^4+a^3+a^3b+a^2b\)
\(=a^2\left(a^2+a+b+b\right)\)
\(=a^2\left(a^2+a+2b\right)\)
\(a^3+4a^2+4a+3\)
a, \(a^4+a^3+a^3b+a^2b=a^3\left(a+1\right)+a^2b\left(a+1\right)=\left(a+1\right)\left(a^2b+a^3\right)=a^2\left(a+1\right)\left(b+a\right)\)
\(a^4+a^3+a^{3b}+a^{2b}\)
\(=a\left(a^3+a^2+1^{3b}+1^{2b}\right)\)
\(a^3+3a^2+4a+12\)
\(=a^2\left(a+3\right)+4\left(a+3\right)\)
\(=\left(a^2+4\right)\left(a+3\right)\)