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a,\(\left(a-b\right)\left(a+2b\right)-\left(b-a\right)\left(2a-b\right)-\left(a-b\right)\left(a+3b\right)\)
\(=\left(a-b\right)\left(a+2b\right)+\left(a-b\right)\left(2a-b\right)-\left(a-b\right)\left(a+3b\right)\)
\(=\left(a-b\right)\left(a+2b+2a-b-a-3b\right)\)
\(=\left(a-b\right)\left(2a-2b\right)\)
\(=\left(a-b\right)2\left(a-b\right)\)
\(=2\left(a-b\right)^2\)
b,\(\left(x+y\right)\left(2x-y\right)+\left(2x-y\right)\left(3x-y\right)-\left(y-2x\right)\)
\(=\left(x+y\right)\left(2x-y\right)+\left(2x-y\right)\left(3x-y\right)+\left(2x-y\right)\)
\(=\left(2x-y\right)\left(x+y+3x-y+1\right)\)
\(=\left(2x-y\right)\left(4x+1\right)\)
c,\(x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)\)
\(=x^2y-x^2z+y^2z-y^2x+z^2\left(x-y\right)\)
\(=x^2y-y^2x-x^2z+y^2z+z^2\left(x-y\right)\)
\(=xy\left(x-y\right)-z\left(x^2-y^2\right)+z^2\left(x-y\right)\)
\(=xy\left(x-y\right)-z\left(x-y\right)\left(x+y\right)+z^2\left(x-y\right)\)
\(=\left(x-y\right)\left(xy-zx-zy+z^2\right)\)
\(=\left(x-y\right)\left(y-z\right)\left(x-z\right)\)
a)5x2y-10xy2
=5xy(x-2y)
b,:4x(2y-z)+7y(z-2y)
=4x(2y-z)-7y(2y-z)
=(2y-z)(4x-7y)
c,:y(x-z)+7(z-x)
=y(x-z)-7(x-z)
=(x-z)(y-7)
d)36-12x+x^2
=x2-2.x.6+62
=(x-6)2
e) (x-5)^2-16
=(x-5)2-42
=(x-5-4)(x-5+4)
=(x-9)(x-1)
f) 8x^3+1/27
=(2x)3+(1/3)3
=(2x+1/3)(4x2+2/3.x+1/9)
\(1,=x\left(x^2-2x+1-y^2\right)=x\left[\left(x-1\right)^2-y^2\right]=x\left(x-y-1\right)\left(x+y-1\right)\\ 2,=\left(x+y\right)^3\\ 3,=\left(2y-z\right)\left(4x+7y\right)\\ 4,=\left(x+2\right)^2\\ 5,Sửa:x\left(x-2\right)-x+2=0\\ \Leftrightarrow\left(x-2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
a) \(\left(x+2\right)^2+2\left(x^2-4\right)+\left(x-2\right)^2\)
\(=\left(x+2\right)^2+\left(x-2\right)\left(x+2\right)+\left(x-2\right)\left(x+2\right)+\left(x-2\right)^2\)
\(=\left(x+2\right)\left(x+2+x-2\right)+\left(x-2\right)\left(x+2+x-2\right)\)
\(=2x\left(x+2\right)+2x\left(x-2\right)\)
\(=2x\left(x+2+x-2\right)\)
\(=2x\cdot2x=4x^2\)
b) \(2x^2-2xy-4y^2\)
\(=\left(2x^2-4xy\right)+\left(2xy-4y^2\right)\)
\(=2x\left(x-2y\right)+2y\left(x-2y\right)\)
\(=\left(2x+2y\right)\left(x-2y\right)\)
\(=2\left(x+y\right)\left(x-2y\right)\)
c) \(x^2-2x-4y^2-4y\)
\(=\left(x^2-4y^2\right)-\left(2x+4y\right)\)
\(=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-2y-2\right)\)
d) \(4x\left(x-2y\right)-8y\left(x-2y\right)\)
\(=\left(x-2y\right)\left(4x-8y\right)\)
\(=4\left(x-2y\right)\left(x-2y\right)\)
\(=4\left(x-2y\right)^2\)
\(2x^2y^3-\frac{x}{4}-4y^6\)
đây là pt bậc 2 của y^3 , ta đặt y^3=z ta được
\(-\left(4z^2+\frac{2.2xz}{2}+\frac{x^2}{4}\right)+\left(\frac{x^2}{4}-\frac{x}{4}\right)\)
\(-\left(2z+\frac{x}{2}\right)^2+\left(\frac{x^2}{4}-\frac{x}{4}\right)\)
\(-\left\{\left(2x+\frac{x}{2}\right)^2-\left(\frac{x^2}{4}-\frac{x}{4}\right)\right\}\)
\(-\left\{\left(2x+\frac{x}{2}+\sqrt{\frac{x^2}{4}-\frac{x}{4}}\right)\left(2x+\frac{x}{2}-\sqrt{\frac{x^2}{4}-\frac{x}{4}}\right)\right\}\)
b) \(64x^3+1=\left(4x+1\right)\left(16x^2-4x+1\right)\)\
c) \(x^3y^6z^9-125=\left(xy^2z^3-5\right)\left(x^2y^4z^6+5xy^2z+25\right)\)
d) \(27x^6-8x^3=x^3\left(27x^3-8\right)=x^3\left(3x-2\right)\left(9x^2+6x+4\right)\)
e) \(x^6-y^6=\left(x^3-y^3\right)\left(x^3+y^3\right)=\left(x-y\right)\left(x^2+xy+y^2\right)\left(x+y\right)\left(x^2-xy+y^2\right)\)
64x3 + 1
= ( 4x )3 + 1
= ( 4x + 1 ) ( 16x2 - 4x + 1 )
Hằng đẳng thức 6 : A3 + B3
27x6 - 8x3
= ( 3x2)3 + ( 2x )3
= ( 3x + 2x ) ( 9x2 - 6x + 4x2 )
HĐT 6
a) Ta có: \(4x\left(2y-z\right)+7y\left(z-2y\right)\)
\(=4x\left(2y-z\right)-7y\left(2y-z\right)\)
\(=\left(4x-7y\right)\left(2y-z\right)\)
b) Ta có: \(2x\left(x+3\right)+\left(3+x\right)\)
\(=\left(2x+1\right)\left(x+3\right)\)