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1. a
$(3x+5)^2=(3x)^2+2.3x.5+5^2$
$=9x^2+30x+25$
1.b
$(6x^2+\frac{1}{3})^2=(6x^2)^2+2.6x^2.\frac{1}{3}+(\frac{1}{3})^2$
$=36x^4+4x^2+\frac{1}{9}$
1.c
$(5x-4y)^2=(5x)^2-2.5x.4y+(4y)^2$
$=25x^2-40xy+16y^2$
1.d
(2x^2y-3y^3x)^2=(2x^2y)^2-2.2x^2y.3y^3x+(3y^3x)^2$
$=4x^4y^2-12x^3y^4+9x^2y^6$
1.e
$(5x-3)(5x+3)=(5x)^2-3^2=25x^2-9$
1.f
$(6x+5y)(6x-5y)=(6x)^2-(5y)^2=36x^2-25y^2$
1.g
$(-4xy-5)(5-4xy)=(-4xy-5)(-4xy+5)$
$=(-4xy)^2-5^2=16x^2y^2-25$
1.h
$(a^2b+ab^2)(ab^2-a^2b)=(ab^2+a^2b)(ab^2-a^2b)$
$=(ab^2)^2-(a^2b)^2=a^2b^4-a^4b^2$
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\(a,A=0,2\left(5x-1\right)-\dfrac{1}{2}\left(\dfrac{2}{3}x+4\right)+\dfrac{2}{3}\left(3-x\right)\)
\(=x-0,2-\dfrac{1}{3}x-2+2-\dfrac{2}{3}x\)
\(=\left(-0,2-2+2\right)+\left(x-\dfrac{1}{3}x-\dfrac{2}{3}x\right)\)
\(=-0,2\)
\(b,B=\left(x-2y\right)\left(x^2+2xy+4y^2\right)-\left(x^3-8y^3+10\right)\)
\(=x^3-8y^3-x^3+8y^3-10\)
\(=-10\)
\(c,C=4\left(x+1\right)^2+\left(2x-1\right)^2-8\left(x-1\right)\left(x+1\right)-4x\)
\(=4\left(x^2+2x+1\right)+\left(4x^2-4x+1\right)-8\left(x^2-1\right)-4x\)
\(=4x^2+8x+4+4x^2-4x+1-8x^2+8-4x\)
\(=13\)
a) \(A=0,2\left(5x-1\right)-\dfrac{1}{2}\left(\dfrac{2}{3}x+4\right)+\dfrac{2}{3}\left(3-x\right)\)
\(A=x-\dfrac{1}{5}-\dfrac{1}{3}x-2+2-\dfrac{2}{3}x\)
\(A=\left(x-\dfrac{1}{3}x-\dfrac{2}{3}x\right)-\left(\dfrac{1}{5}+2-2\right)\)
\(A=-\dfrac{1}{5}\)
Vậy: ...
b) \(B=\left(x-2y\right)\left(x^2+2xy+4y^2\right)-\left(x^3-8y^3+10\right)\)
\(B=\left[x^3-\left(2y\right)^3\right]-\left[x^3-\left(2y\right)^3\right]-10\)
\(B=-10\)
Vậy: ...
c) \(4\left(x+1\right)^2+\left(2x-1\right)^2-8\left(x+1\right)\left(x-1\right)-4x\)
\(=4\left(x^2+2x+4\right)+\left(4x^2-4x+1\right)-8\left(x^2-1\right)-4x\)
\(=4x^2+8x+4+4x^2-4x+1-8x^2+8-4x\)
\(=\left(4x^2+4x^2-8x^2\right)+\left(8x-4x-4x\right)+\left(4+1+8\right)\)
\(=13\)
Vậy:...
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g: \(=\dfrac{x^2+2x-x^2-4x-2x+4}{x\left(x-2\right)\left(x+2\right)}=\dfrac{-4x+4}{x\left(x-2\right)\left(x+2\right)}\)
h: \(=\dfrac{2x^2+1-x^2+1-x^2+x-1}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{x+1}{\left(x+1\right)\left(x^2-x+1\right)}=\dfrac{1}{x^2-x+1}\)
\(e,=\dfrac{1}{x-1}-\dfrac{2x}{\left(x^2+1\right)\left(x-1\right)}=\dfrac{x^2-2x+1}{\left(x^2+1\right)\left(x-1\right)}=\dfrac{\left(x-1\right)^2}{\left(x^2+1\right)\left(x-1\right)}=\dfrac{x-1}{x^2+1}\\ f,=\dfrac{3x-1}{2\left(3x+1\right)}+\dfrac{3x+1}{2\left(3x-1\right)}-\dfrac{6x}{\left(3x-1\right)\left(3x+1\right)}\\ =\dfrac{9x^2-6x+1+9x^2+6x+1-12x}{2\left(3x-1\right)\left(3x+1\right)}=\dfrac{2\left(3x-1\right)^2}{2\left(3x-1\right)\left(3x+1\right)}=\dfrac{3x-1}{3x+1}\)
\(g,=\dfrac{x}{x\left(x-2\right)}-\dfrac{x^2+4x}{x\left(x-2\right)\left(x+2\right)}-\dfrac{2}{x\left(x+2\right)}\\ =\dfrac{x^2+2x-x^2-4x-2x+4}{x\left(x-2\right)\left(x+2\right)}=\dfrac{-4x+4}{x\left(x-2\right)\left(x+2\right)}\\ h,=\dfrac{2x^2+1-x^2+1-x^2+x-1}{\left(x+1\right)\left(x^2-x+1\right)}=\dfrac{x+1}{\left(x+1\right)\left(x^2-x+1\right)}=\dfrac{1}{x^2-x+1}\)
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e: \(E=\dfrac{x^2-9-x^2+4-x^2+9}{\left(x+3\right)\left(x-2\right)}\)
\(=\dfrac{x+2}{x+3}\)
a: \(A=\dfrac{4x^2+x^2-2x+1+x^2+2x+1}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{6x^2+2}{\left(x-1\right)\left(x+1\right)}\)
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Lời giải:
Vì $D,E$ lần lượt là trung điểm $AB,AC$ nên $DE$ là đường trung bình của tam giác $ABC$ ứng với cạnh $BC$
$\Rightarrow DE\parallel BC$ và $DE=\frac{BC}{2}=2$ (cm)
Vì $DE\parallel BC$ nên $DECB$ là hình thang
Xét hình thang $DECB$ có $M,N$ lần lượt là trung điểm của cạnh bên $BD, CE$ nên $MN$ là đường trung bình của hình thang $DECB$
$\Rightarrow MN=\frac{DE+BC}{2}=\frac{2+4}{2}=3$ (cm)
Hình vẽ:
![](data:image/png;base64,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)