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dài quá mình làm 3 câu đầu thôi nhé!
a)7x^2-14xy
=7x(x-2y)
b) 3x^2-6xy+3y^2
=3(x^2-2xy+y^2)
c) x^2-4z^2-2xy+y^2
=(x^2-2xy+y^2)-4z^2
=(x-y-2z)(x-y+2z)
=3(x-y)^2
c)
a ) \(6a^2y-3aby+4a^2x-2abx\)
\(=3ay\left(2a-b\right)+2ax\left(2a-b\right)\)
\(=\left(3ay+2ax\right)\left(2a-b\right)\)
\(=a\left(3y+2x\right)\left(2a-b\right)\)
b ) \(ax-bx-2cx-2a+2b+4c\)
\(=a\left(x-2\right)-b\left(x-2\right)-2c\left(x-2\right)\)
\(=\left(a-b-2c\right)\left(x-2\right)\)
c ) \(x^9+1\)
\(=\left(x^3\right)^3+1\)
\(=\left(x^3+1\right)\left(x^6-x^2+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1\right)\left(x^6-x^3+1\right)\)
d ) \(25x^2-20xy+4y^2\)
\(=\left(5x-2y\right)^2\)
e ) \(x^2+2xy+y^2-25\)
\(=\left(x+y\right)^2-25\)
\(=\left(x+y-5\right)\left(x+y+5\right)\)
Bài 2 :
Câu a : \(y\left(y^3+y^2-y-2\right)-\left(y^2-2\right)\left(y^2+y+1\right)\)
\(=y^4+y^3-y^2-2y-y^4-y^3-y^2+2y^2+2y+2\)
\(=2\) \(\Rightarrow\) ko phụ thuộc vào biến .
Câu b : \(\left(2x+3\right)\left(4x^2-6x+9\right)-2\left(4x^3-1\right)\)
\(=8x^3-12x^2+18x+12x^2-18x+27-8x^3+2\)
\(=29\Rightarrow\) ko thuộc vào biến
Câu c : \(3x\left(x+5\right)-\left(3x+18\right)\left(x-1\right)\)
\(=3x^2+15x-3x^2+3x-18x+18\)
\(=18\) \(\Rightarrow\) ko thuộc vào biến
Câu d : \(\left(2x+6\right)\left(4x^2-12x+36\right)-8x^3+5\)
\(=8x^3-24x^2+72x+24x^2-72x+216-8x^3+5\)
\(=221\) \(\Rightarrow\) không thuộc vào biến
câu 1) a) \(\left(x^2+2xy+y^2\right)\left(x+y\right)=\left(x+y\right)^2\left(x+y\right)=\left(x+y\right)^3\)
b) \(y\left(y^3+y^2-3y-2\right)+\left(y^2-2\right)\left(y^2+y-1\right)\)
\(=y^4+y^3-3y^2-2y+y^4+y^3-y^2-2y^2-2y+2\)
\(=2y^4+2y^3-6y^2-4y+2=2y\left(y^3+y^2-3y-2\right)+2\)
\(=2y\left(y+2\right)\left(y^2-y-1\right)+2=2\left(y^2+2y\right)\left(y^2-y-1\right)+2\)
\(=2\left(y^2+2y\right)\left(y^2-y-1+1\right)=2\left(y^2+2y\right)\left(y^2-y\right)\)
c) \(6x^2-\left(2x+5\right)\left(3x-2\right)=6x^2-\left(6x^2-4x+15x-10\right)\)
\(\Leftrightarrow6x^2-6x^2+4x-15x+10=-11x+10\)
d) \(\left(2x-1\right)\left(3x+1\right)+\left(3x+4\right)\left(3-2x\right)\)
\(\)\(=6x^2+2x-3x-1+9x-6x^2+12-8x=11\)
e) \(\left(3x-5\right)\left(7-5x\right)-\left(5x+2\right)\left(2-3x\right)\)
\(=21x-15x^2-35+25x-\left(10x-15x^2+4-6x\right)\)
\(21x-15x^2-35+25x-10x+15x^2-4+6x=42x-39\)
1
a, 2x2+4x+2-2y2 = 2(x2+2x+1-y2)= 2[(x+1)2-y2 ] = 2(x-y+1)(x+y+1)
b, 2x - 2y - x2 + 2xy - y2= 2(x -y) - (x2 - 2xy + y2) = 2(x-y)-(x-y)2=(x-y)(2-x+y)
c, x2-y2-2y-1=x2-(y2+2y+1)=x2-(y+1)2=(x-y-1)(x+y+1)
d, x2-4x-2xy-4y+y2= x2-2xy+y2-4x-4y=(x-y)
2.
a, x2-3x+2=x2-x-2x+2=x(x-1)-2(x-1)=(x-2)(x-1)
b, x2+5x+6=x2+2x+3x+6=x(x+2)+3(x+2)=(x+3)(x+2)
c, x2+6x-6=
\(10x\left(x-y\right)-6y\left(y-x\right)\)
\(=10x\left(x-y\right)+6x\left(x-y\right)\)
\(=\left(10x+6x\right)\left(x-y\right)\)
\(c,3x^2+5y-3xy-5x\)
\(=\left(3x^2-3xy\right)+\left(5y-5x\right)\)
\(=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(3x-5\right)\left(x-y\right)\)
\(e,27+27x+9x^2=3\left(9+9x+x^2\right)\)
\(x^6-y^6=\left(x^3-y^3\right)\left(x^3+y^3\right)=\left(x-y\right)\left(x^2+xy+y^2\right)\left(x+y\right)\left(x^2-xy+y^2\right)\)
\(x^2+x+y^2+y+2xy=\left(x+y\right)^2+\left(x+y\right)=\left(x+y\right)\left(x+y+1\right)\)
\(-x^2+5x+2xy-5y-y^2=5\left(x-y\right)-\left(x-y\right)^2=\left(x-y\right)\left(5-x+y\right)\)
\(y^2+2yt-v^2+2vu+t^2-u^2==\left(y+t\right)^2-\left(v-u\right)^2=\left(y+t+v-u\right)\left(y+t-v+u\right)\)
tui làm tip 1 câu, các câu khác tt, bn p.an làm đúng mà bn k tích nên chẳng ai muon lam cho ke vo on dau
b) = (x+y)( x+y+1)