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Câu 1:
a/ (-5x3)(2x2+3x-5)
=-10x5-15x4+25x3
b/(2x-1)x
=2x2-x
c/(x-y)(3x2+4xy)
=3x3+4x2y-3x2y-4xy2
=3x3 +x2y-4xy2
Câu 2:
a/ x3-2x2+x
=x(x2-2x+1)
=x(x-1)2
b/x2-x-12
=x2 +3x-4x-12
=(x2 +3x)+(-4x-12)
=x(x+3)-4(x+3)
=(x+3)(x-4)
c/ 2x-6
=2(x-3)
e/ x2+4x+4-y2
=(x2+4x+4)-y2
=(x+2)2-y2
=(x+2-y)(x+2+y)
d/ x2-2xy+y2-16
=(x2-2xy+y2)-16
=(x-y)2-16
=(x-y-4)(x-y+4)
Câu 3:
a: \(=\dfrac{5xy-4+3xy+4}{2x^2y^3}=\dfrac{8xy}{2x^2y^3}=\dfrac{4}{xy^2}\)
b: \(=\dfrac{y-12}{6\left(y-6\right)}+\dfrac{6}{y\left(y-6\right)}\)
\(=\dfrac{y^2-12y+36}{6y\left(y-6\right)}=\dfrac{y-6}{6y}\)
c: \(=\dfrac{3x+1-2x+3}{x+y}=\dfrac{x+4}{x+y}\)
d: \(=\dfrac{4x+7+5x+7}{9}=\dfrac{9x+14}{9}\)
e: \(=\dfrac{5\left(x+2\right)}{2\left(2x-1\right)}\cdot\dfrac{-2\left(x-2\right)}{x+2}=\dfrac{-5\left(x-2\right)}{2x-1}\)
\(3x\left(x-5\right)-x\left(4+3x\right)=43\)
\(\Leftrightarrow3x^2-15x-4x-3x^2=43\)
\(\Leftrightarrow-19x=43\)
\(\Leftrightarrow x=\frac{-43}{19}\)
a, \(x^6-x^4+2x^3+2x^2=x^2\left(x^4-x^2+2x+2\right)=x^2\left[x^2\left(x^2-1\right)+2\left(x+1\right)\right]\)
\(=x^2\left[x^2\left(x-1\right)\left(x+1\right)+2\left(x+1\right)\right]=x^2\left[\left(x+1\right)\left(x^3+x^2+2\right)\right]\)
\(=x^2\left(x+1\right)\left[\left(x^3+1\right)-\left(x^2-1\right)\right]=x^2\left(x+1\right)\left(x^2-2x+2\right)\)
b, \(\left(x+y\right)^3-\left(x-y\right)^3=\left(x+y-x+y\right)\left[\left(x+y\right)^2+\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\right]\)
\(=2y\left[\left(x+y\right)\left(x+y+x-y\right)+\left(x-y\right)^2\right]\)\(=2y\left[2x\left(x+y\right)+\left(x-y\right)^2\right]\)
\(=2y\left(2x^2+2xy+x^2-2xy+y^2\right)\)\(=2y\left(3x^2+y^2\right)\)
c, \(x^3-3x^2+3x-1-y^3=\left(x-1\right)^3-y^3=\left(x-1-y\right)\left[\left(x-1\right)^2+\left(x-1\right)y+y^2\right]\)
\(=\left(x-1-y\right)\left[x^2-2x+1+xy-y+y^2\right]\)
d, \(x^5+x^4+1=x^5+x^4+x^3-x^3+1\)
\(=x^3\left(x^2+x+1\right)-\left(x-1\right)\left(x^2+x+1\right)\)\(=\left(x^2+x+1\right)\left(x^3-x+1\right)\)
e, \(4x^4+81=\left(2x^2\right)^2+36x^2+9^2-36x^2=\left(2x^2+9\right)^2-\left(6x\right)^2\)
\(=\left(2x^2+9+6x\right)\left(2x^2+9-6x\right)\)
d, \(64x^4+y^4=\left(8x^2\right)^2+16x^2y^2+\left(y^2\right)^2-16x^2y^2=\left(8x^2+y^2\right)^2-\left(4xy\right)^2=\left(8x^2+y^2+4xy\right)\left(8x^2+y^2-4xy\right)\)