Bài 1: Nhân đơn thức với đa thức

\(=-x^2y^3\cdot2x^{n-2}y^n+x^2y^3\cdot3x^ny^{n-3}-x^2y^3\cdot x^{n-2}y^{n-3}\)

\(=-2x^ny^{n+3}+3x^{n+2}y^n-x^ny^n\)

\(-\dfrac{2}{3}\left(x^2y^2\right)^2+\dfrac{1}{3}xy^2\cdot0,75x-3xy\cdot\left(-2x\right)\)

\(=-\dfrac{2}{3}x^4y^4+\dfrac{1}{3}xy^2\cdot\dfrac{3}{4}x-3xy\cdot\left(-2x\right)\)

\(=-\dfrac{2}{3}x^4y^4+\left(\dfrac{1}{3}\cdot\dfrac{3}{4}\right)\left(x\cdot x\right)y^2-\left(3\cdot-2\right)\left(x\cdot x\right)y\)

\(=-\dfrac{2}{3}x^4y^4+\dfrac{1}{4}x^2y^2+6x^2y\)

giúp tui bài này zới ạ

4:

1: \(=x^3-x^2-x^3-2x^2-x-2=-3x^2-x-2\)

2: \(=x^2-xy^2-x^2y-x^2+y^2+y\)

=-xy^2-x^2y+y^2+y

3: \(=x^3+26x-5x^2-130+5-25x-x+5x^2\)

=x^3-125

4: \(=x^3+xy-x^2y-y^2-x^3-xy^2+x^2+y^2\)

=-x^2y-xy^2+x^2+xy

5: \(=6x^2-7x+2-15x^2-13x-2\)

=-9x^2-20x

6: \(=6x^2+23x-55-6x^2-23x-21\)

=-76

7: \(=2x^2-5x-12+x^2-7x+10=3x^2-12x-2\)

8: \(=48x^2-32x+5+3x-48x^2-7+112x\)

=83x-2

\(\Leftrightarrow12y-36=17\\ \Leftrightarrow12y=17+36=53\\ \Rightarrow y=\dfrac{53}{12}\)

12(y-3)=17

\(\Leftrightarrow\) 12y - 36 = 17

\(\Leftrightarrow\) 12y = 17 + 36

\(\Leftrightarrow\) 12y = 53

\(\Leftrightarrow\) y = \(\dfrac{53}{12}\)

\(12(y-3)=17\)

\(\Leftrightarrow12y=17+36\)

\(\Leftrightarrow12y=53\)

\(\Leftrightarrow y=53:12\)

\(\Leftrightarrow y=\dfrac{53}{12}\)

\(a,\)Thay \(x=-1;y=0,5\) vào \(p=x^3y-14y^3-6xy^2+y+2\)

\(\Rightarrow p=\left(-1\right)^3.0,5-14.0,5^3-6.\left(-1\right).0,5^2+0,5+2\)

\(=-0,5-1,75+1,5+0,5+2\)

\(=1,75\)

\(b,\)Thay \(x=0,2;y=-1,2\) vào \(q=15x^2y-5xy^2+7xy-21\)

\(\Rightarrow p=15.0,2^2.\left(-1,2\right)-5.0,2.\left(-1,2\right)^2+7.0,2.\left(-1,2\right)-21\)

\(=-0,72-1,44-1,68-21\)

\(=-24,84\)

2x - 3 = 0 

\(\Leftrightarrow\) 2x  = 3

\(\Leftrightarrow\)   x = \(\dfrac{3}{2}\) 

S = \(\left\{\dfrac{3}{2}\right\}\)

\(2x-3=0\\ \Leftrightarrow2x=3\\ \Leftrightarrow x=\dfrac{3}{2}\\ S=\left\{\dfrac{3}{2}\right\}\)

2x-3=0

2x=0+3

2x=3

x=3:2

x=1.5

TH1: x>=-5

=>D=3x+2+x+5=4x+7

TH2: x<-5

D=3x+2-x-5=2x-3

\(a,\\ \dfrac{x-23}{24}+\dfrac{x-23}{25}=\dfrac{x-23}{26}+\dfrac{x-23}{27}\\ \Leftrightarrow\dfrac{x-23}{24}+\dfrac{x-23}{25}-\dfrac{x-23}{26}-\dfrac{x-23}{27}=0\\ \Leftrightarrow\left(x-23\right)\left(\dfrac{1}{24}+\dfrac{1}{25}-\dfrac{1}{26}-\dfrac{1}{27}\right)=0\)

mà `1/24+1/25-1/26-1/27 \ne 0`

nên `x-23=0`

`x=23`

\(c,\\ \dfrac{x+1}{2004}+\dfrac{x+2}{2003}=\dfrac{x+3}{2002}+\dfrac{x+4}{2001}\\ \Leftrightarrow\left(\dfrac{x+1}{2004}+1\right)+\left(\dfrac{x+2}{2003}+1\right)=\left(\dfrac{x+3}{2002}+1\right)+\left(\dfrac{x+4}{2001}+1\right)\\ \Leftrightarrow\dfrac{x+2005}{2004}+\dfrac{x+2005}{2003}=\dfrac{x+2005}{2002}+\dfrac{x+2005}{2001}\\ \Leftrightarrow\dfrac{x+2005}{2004}+\dfrac{x+2005}{2003}-\dfrac{x+2005}{2002}-\dfrac{x+2005}{2001}=0\\ \Leftrightarrow\left(x+2005\right)\left(\dfrac{1}{2004}+\dfrac{1}{2003}-\dfrac{1}{2002}-\dfrac{1}{2001}\right)=0\\ \Leftrightarrow x+2005=0\left(\dfrac{1}{2004}+\dfrac{1}{2003}-\dfrac{1}{2002}-\dfrac{1}{2001}\ne0\right)\\ \Rightarrow x=-2005\)

\(e,\\ \dfrac{x-45}{55}+\dfrac{x-47}{53}=\dfrac{x-55}{45}+\dfrac{x-53}{47}\\ \Leftrightarrow\left(\dfrac{x-45}{55}-1\right)+\left(\dfrac{x-47}{53}-1\right)-\left(\dfrac{x-55}{45}-1\right)-\left(\dfrac{x-53}{47}-1\right)=0\\ \Leftrightarrow\dfrac{x-100}{55}+\dfrac{x-100}{53}-\dfrac{x-100}{45}-\dfrac{x-100}{47}=0\\ \Leftrightarrow\left(x-100\right)\left(\dfrac{1}{55}+\dfrac{1}{53}-\dfrac{1}{45}-\dfrac{1}{47}\right)=0\\ \Leftrightarrow x-100=0\left(\dfrac{1}{55}+\dfrac{1}{53}-\dfrac{1}{45}-\dfrac{1}{47}\ne0\right)\\ \Rightarrow x=100\)

\(\dfrac{4x}{x^2-25}+\dfrac{3}{x+5}-\dfrac{2}{x-5}=\dfrac{4x}{\left(x+5\right)\left(x-5\right)}+\dfrac{3}{x+5}-\dfrac{2}{x-5}\)

\(=\dfrac{4x+3x-15-2x-10}{\left(x+5\right)\left(x-5\right)}=\dfrac{5x-25}{\left(x+5\right)\left(x-5\right)}=\dfrac{5}{x+5}\)

1: \(=\dfrac{4x+3x-15-2x-10}{\left(x-5\right)\left(x+5\right)}=\dfrac{5x-25}{\left(x-5\right)\left(x+5\right)}=\dfrac{5}{x+5}\)

2: |A|=A

=>A>=0

=>5/x+5>=0

=>x+5>0

=>x>-5