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\(xy+3z+xz+3y\)
\(=\left(xy+3y\right)+\left(xz+3z\right)\)
\(=y\left(x+3\right)+z\left(x+3\right)\)
\(=\left(y+z\right)\left(x+3\right)\)
\(11x-x^2+11y-xy\)
\(=x\left(11-x\right)+y\left(11-x\right)\)
\(=\left(x+y\right)\left(11-x\right)\)
\(xy+3z+xz+3y\)
\(=\left(xy+xz\right)+\left(3y+3z\right)\)
\(=x\left(y+z\right)+3\left(y+z\right)\)
\(=\left(y+z\right)\left(x+3\right)\)
\(11x-x^2+11y-xy\)
\(=\left(11x+11y\right)-\left(x^2+xy\right)\)
\(=11\left(x+y\right)-x\left(x+y\right)\)
\(=\left(x+y\right)\left(11-x\right)\)
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) \(\left(x+y\right)^3-x^3-y^3\)
\(=\left(x+y\right)^3-\left(x+y\right)\left(x^2-xy+y^2\right)\)
\(=\left(x+y\right)\left[\left(x+y\right)^2-x^2+xy-y^2\right]\)
\(=\left(x+y\right)\left(x^2+2xy+y^2-x^2+xy-y^2\right)\)
\(=3xy\left(x+y\right)\)
b) \(x^2+y^2+2xy+yz+xz\)
\(=\left(x^2+2xy+y^2\right)+\left(yz+xz\right)\)
\(=\left(x+y\right)^2+z\left(x+y\right)\)
\(=\left(x+y\right)\left(x+y+z\right)\)
c) \(x^2-10xy-1+25y^2\)
\(=\left(x^2-10xy+25y^2\right)-1\)
\(=\left(x-5y\right)^2-1\)
\(=\left(x-5y-1\right)\left(x-5y+1\right)\)
d) \(ax^2-ax+bx^2-bx+a+b\)
\(=(ax^2+bx^2)-(ax+bx)+(a+b)\)
\(=x^2(a+b)-x(a+b)+(a+b)\)
\(=(a+b)(x^2-x+1)\)
e)\(x^2-2y+3xz+x-2y+3z\)
\(=(x^2+x)-(2xy+2y)+(3xz+3z)\)
\(=x(x+1)-2y(x-1)+3z(x+1)\)
\(=(x+1)(x-2y+3z)\)
f) \(xyz-xy-yz-xz+x+y+z-1\)
\(=(xyz-xy)-(yz-y)-(xz-x)+(z-1)\)
\(=xy(z-1)-y(z-1)-x(z-1)+(z-1)\)
\(=(z-1)(xy-y-x+1)\)
\(=(z-1)[y(x-1)-(x-1)]\)
\(=(z-1)(x-1)(y-1)\)
_Học tốt_
Bài giải:
a) x2 – xy + x – y = (x2 – xy) + (x - y)
= x(x - y) + (x -y)
= (x - y)(x + 1)
b) xz + yz – 5(x + y) = z(x + y) - 5(x + y)
= (x + y)(z - 5)
c) 3x2 – 3xy – 5x + 5y = (3x2 – 3xy) - (5x - 5y)
= 3x(x - y) -5(x - y) = (x - y)(3x - 5).
\(a) x^2 - xy+x-y\) \(= (x^2 - xy) + ( x- y) \)
\(=x(x-y) + (x-y)\)
\(= (x-y) (x+1)\)
\(b) xz + yz - 5(x+y)\) \(= (xz + yz) - 5(x+y)\)
\(= z(x+y) - 5(x+y)\)
\(= (x+y) (z-5)\)
\(c) 3x^2 - 3xy - 5x +5y = (3x^2-3xy) - (5x-5y)\)
\(= 3x(x-y) - 5(x-y)\)
\(= (x-y)(3x-5)\)
a) xy(x + y) + yz(y + z) + xz(z + x) + 3xyz
= xy(X + y + z) + yz(x + y + z) + xz(X + y + z)
= (x + y +z)(xy + yz+ xz)
b) xy(x + y) - yz(y + z) - xz(z - x)
= x2y + xy2 - y2z - yz2 - xz2 + x2z
= x2(y + z) - yz(y + z) + x(y2 - z2)
= x2(y + z) - yz(y + z) + x(y + z)(y - z)
= (y + z)(x2 - yz + xy - xz)
= (y + z)[x(x + y) - z(x + y)]
= (y + z)(x + y)(x - z)
c) x(y2 - z2) + y(z2 - x2) + z(x2 - y2)
= x(y - z)(y + z) + yz2 - yx2 + x2z - y2z
= x(y - z)(y + z) - yz(y - z) - x2(y - z)
= (y - z)((xy + xz - yz - x2)
= (y - z)[x(y - x) - z(y - x)]
= (y - z)(x - z)(y -x)
a) \(a^4+a^3+a^2+a=a^3\left(a+1\right)+a\left(a+1\right)=a\left(a+1\right)\left(a^2+1\right)\)
b) \(x^4+x^2+x=x\left(x^3+x+1\right)\)
c) \(xy+z+y+xz=y\left(x+1\right)+z\left(x+1\right)=\left(x+1\right)\left(y+z\right)\) đề vậy còn ra
\(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)
\(=\left(x^2y+xy^2+xyz\right)+\left(x^2z+xz^2+xyz\right)+\left(y^2z+yz^2+xyz\right)\)
\(=xy\left(x+y+z\right)+xz\left(x+y+z\right)+yz\left(x+y+z\right)\)
\(=\left(x+y+z\right)\left(xy+xz+yz\right)\)
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.
a) \(xy+xz+3y+3z=x\left(y+z\right)+3\left(y+z\right)=\left(x+3\right)\left(y+z\right)\)
b) \(xy-xz+y-z=x\left(y-z\right)+\left(y-z\right)\left(x+1\right)\left(y-z\right)\)
c) \(15x+15y-x^2-xy=15\left(x+y\right)-x\left(x+y\right)=\left(15-x\right)\left(x+y\right)\)
d) \(x^2-xy-10x+10y=x\left(x-y\right)-10\left(x-y\right)=\left(x-10\right)\left(x-y\right)\)
b) \(xy-xz+y-z=x\left(y-z\right)+\left(y-z\right)=\left(x+1\right)\left(y-z\right)\)