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a: =-1/5x^5y^2
b: =-9/7xy^3
c: =7/12xy^2z
d: =2x^4
e: =3/4x^5y
f: =11x^2y^5+x^6
a) P + Q = (x² + 2x³ - xy² + 5) + (x³ + xy² - 2x²y - 6)
= x² + 2x³ - xy² + 5 + x³ + xy² - 2x²y - 6
= (2x³ + x³) + x² + (-xy² + xy²) - 2x²y + (5 - 6)
= 3x³ + x² - 2x²y - 1
b) Q = P + N
N = Q - P
= (x³ + xy² - 2x²y - 6) - (x² + 2x³ - xy² + 5)
= x³ + xy² - 2x²y - 6 - x² - 2x³ + xy² - 5
= (x³ - 2x³) + (xy² + xy²) - 2x²y - x² + (-6 - 5)
= -x³ + 2xy² - 2x²y - x² - 11
Vậy N = -x³ + 2xy² - 2x²y - x² - 11
bài 1: ĐKXĐ: \(x\notin\left\{2;-2\right\}\)
\(\dfrac{x}{x+2}-\dfrac{x}{x-2}\)
\(=\dfrac{x\left(x-2\right)-x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x^2-2x-x^2-2x}{\left(x-2\right)\left(x+2\right)}=-\dfrac{4x}{x^2-4}\)
Bài 2:
1: \(x^2y^2-8-1\)
\(=x^2y^2-9\)
\(=\left(xy-3\right)\left(xy+3\right)\)
2: \(x^3y-2x^2y+xy-xy^3\)
\(=xy\cdot x^2-xy\cdot2x+xy\cdot1-xy\cdot y^2\)
\(=xy\left(x^2-2x+1-y^2\right)\)
\(=xy\left[\left(x-1\right)^2-y^2\right]\)
\(=xy\left(x-1-y\right)\left(x-1+y\right)\)
3: \(x^3-2x^2y+xy^2\)
\(=x\cdot x^2-x\cdot2xy+x\cdot y^2\)
\(=x\left(x^2-2xy+y^2\right)=x\left(x-y\right)^2\)
4: \(x^2+2x-y^2+1\)
\(=\left(x^2+2x+1\right)-y^2\)
\(=\left(x+1\right)^2-y^2\)
\(=\left(x+1+y\right)\left(x+1-y\right)\)
5: \(x^2+2x-4y^2+1\)
\(=\left(x^2+2x+1\right)-4y^2\)
\(=\left(x+1\right)^2-4y^2\)
\(=\left(x+1-2y\right)\left(x+1+2y\right)\)
6: \(x^2-6x-y^2+9\)
\(=\left(x^2-6x+9\right)-y^2\)
\(=\left(x-3\right)^2-y^2=\left(x-3-y\right)\left(x-3+y\right)\)
a: =>A-B=3x^2y-4xy^2+x^2y-2xy^2=4x^2y-6xy^2
b: =>B-A=-7xy^2+8x^2y-5xy^2+6x^2y=-12xy^2+14x^2y
=>A-B=12xy^2-14x^2y
c: =>B-A=8x^2y^3-4x^3y-3x^2y^3+5x^3y^2=5x^2y^3+x^3y^2
=>A-B=-5x^2y^3-x^3y^2
d: =>A-B=2x^2y^3-7x^3y+6x^2y^3+3x^3y^2=8x^2y^3-7x^3y+3x^3y^2
Biến đổi mỗi đa thức theo hướng làm xuất hiện thừa số x+y-2 \(M=x^3+x^2y-2x^2-xy-y^2+3y+x-1\)
\(M=x^3+x^2y-2x^2-xy-y^2+\left(2y+y\right)+x-\left(-2+1\right)\)
\(M=\left(x^3+x^2y-2x^2\right)-\left(xy+y^2-2y\right)+\left(x+y-2\right)+1\)
\(M=\left(x^2.x+x^2.y-2x^2\right)-\left(x.y+y.y-2y\right)+\left(x+y-2\right)+1\)
\(M=x^2.\left(x+y-2\right)-y.\left(x+y-2\right)+\left(x+y-2\right)+1\)
\(M=x^2.0+y.0+0+1\)
\(M=1\)
\(N=x^3+x^2y-2x^2-xy^2+x^2y+2xy+2y+2x-2\)
\(N=x^3+x^2y-2x^2-xy^2+x^2y+2xy+2y+2x-\left(-4+2\right)\)
\(N=\left(x^3+x^2y-2x^2\right)-\left(x^2y+xy^2-2xy\right)+\left(2x+2y-4\right)+2\)
\(N=\left(x^2x+x^2y-2x^2\right)-\left(xyx+xyy-2xy\right)+\left(2x+2y-4\right)+2\)
\(N=x^2\left(x+y-2\right)-xy\left(x+y-2\right)+2\left(x+y-2\right)+2\)
\(N=x^2.0-xy.0+2.0+2\)
\(N=2\)
\(P=x^4+2x^3y-2x^3+x^2y^2-2x^2y-x\left(x+y\right)+2x+3\)
\(P=\left(x^4+x^3y-2x^3\right)+\left(x^3y+x^2y^2-2x^2y\right)-\left(x^2+xy-2x\right)+3\)\(P=\left(x^3x+x^3y-2x^3\right)+\left(x^2y.x+x^2yy-2x^2y\right)-\left(xx+xy-2x\right)+3\)
\(P=x^3\left(x+y-2\right)+x^2y\left(x+y-2\right)-x\left(x+y-2\right)+3\)
\(P=x^3.0+x^2y.0-x.0+3\)
\(P=3\)
Tích mình nha!
a: (3x^2-4)(x+3y)
=3x^2*x+3x^2*3y-4x-4*3y
=3x^3+9x^2y-4x-12y
b: (c+3)(x^2+3x)
=c*x^2+c*3x+3x^2+9x
=cx^2+3cx+3x^2+9x
c: (xy-1)(xy+5)
=xy*xy+5xy-xy-5
=x^2y^2+4xy-5
d: (3x+5y)(2x-7y)
=3x*2x-3x*7y+5y*2x-5y*7y
=6x^2-21xy+10xy-35y^2
=6x^2-11xy-35y^2
e: -(x-1)(-x^2+2y)
=(x-1)(x^2-2y)
=x^3-2xy-x^2+2y
f: (-x^2+2y)(x^2+2y)
=(2y)^2-x^4
=4y^2-x^4
a) `A+B=x^2y+2x^3-xy^2+5+x^3+xy^2-2x^2y-6`
`=(x^2y-2x^2y)+(2x^3+x^3)+(-xy^2+xy^2)+(5-6)`
`=3x^3-x^2y-1`
``
b) `B=A+C`
`<=>C=B-A`
`<=>C=x^3+xy^2-2x^2y-6-(x^2y+2x^3-xy^2+5)`
`<=>C =x^3+xy^2-2x^2y-6-x^2y-2x^3+xy^2-5`
`<=> C=(x^3-2x^3)+(xy^2+xy^2)+(-2x^2y-x^2y)+(-6-5)`
`<=>C=-x^3+2xy^2-3x^2y-11`