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Bài 2:
1) \(7x^2+2x=0\)
\(\Leftrightarrow x\left(7x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\7x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{2}{7}\end{matrix}\right.\)
2) \(2x\left(x-9\right)+5\left(x-9\right)=0\)
\(\Leftrightarrow\left(x-9\right)\left(2x+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-9=0\\2x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=9\\x=-\dfrac{5}{2}\end{matrix}\right.\)
3) \(x^2+8x+16=0\)
\(\Leftrightarrow\left(x+4\right)^2=0\)
\(\Leftrightarrow x+4=0\)
\(\Leftrightarrow x=-4\)
Bài 1:
2) \(24x-18y+30=6\left(4x-3y+5\right)\)
5) \(x^2+14x+49=\left(x+7\right)^2\)
6) \(27x^3+y^3=\left(3x+y\right)\left(9x^2-3xy+y^2\right)\)
a) 2x(y-2009)+5y(y-2009)
=(y-2009)(2x+5y)
b) 35x(y-8)-14y(8-y)
=35x(y-8)+14y(y-8)
=7(y-8)(5x+2y)
c) 15x^2 +10xy =5x(3x+2y)
d)24x-18y+30= 6(4x+3y+10)
e) x^2 +14x+49
= x^2 +2.7.x+ 7^2
=(x+7)^2
i) x^2 -x - y^2 - y
=(x^2 -y^2)-(x+y)
=(x-y)(x+y)-(x+y)
=(x+y)(x-y-1)
k) x^2 -2xy+y^2 -z^2
=(x^2 -2xy+y^2) -z^2
=(x-y)^2 -z^2
= (x-y-z)(x-y+z)
a) \(2x\left(y-2009\right)+5y\left(y-2009\right)\) \(=\left(y-2009\right)\left(2x+5y\right)\)
b) \(35x(y-8)-14y(8-y)\) \(=35x\left(y-8\right)+14y\left(y-8\right)\)
\(=\left(y-8\right)\left(35x+14y\right)\)
\(=\left(y-8\right).7\left(5x+2y\right)\)
c) \(15x^2+10xy=5x\left(3x+2y\right)\)
d) \(24x-18y+30=3\left(8x-6y+10\right)\)
e) \(x^2+14x+49=x^2+2.7.x+7^2\)
\(=\) \((x+7)^2\)
g) \(27x^3+y^3\) \(=\left(3x+y\right)\left(9x^2-3xy+y^2\right)\)
h) \(8x^3-\dfrac{1}{125}y^3=\left(2x-\dfrac{1}{5}y\right)\left(4x^2+\dfrac{2}{5}xy+\dfrac{1}{25}y^2\right)\)
i) \(x^2-x-y^2-y=\left(x^2-y^2\right)-\left(x+y\right)\)
\(=\left(x-y\right)\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-1\right)\)
k) \(x^2-2xy+y^2-z^2=\left(x^2-2xy+y^2\right)-z^2\)
\(=\left(x-y\right)^2-z^2\)
\(=\left(x-y-z\right)\left(x-y+z\right)\)
- HỌC TỐT NHA BẠN YÊU ^^ -
7, \(27x^3+y^3=\left(3x+y\right)\left(9x^2-3xy+y^2\right)\)
8, \(8x^3-\frac{1}{125}y^3=\left(2x-\frac{1}{5}y\right)\left(4x^2+\frac{2}{5}xy+\frac{1}{25}y^2\right)\)
9, ĐK x >= 0
\(x-2\sqrt{x}-3=x-3\sqrt{x}+\sqrt{x}-3\)
\(=\sqrt{x}\left(\sqrt{x}+1\right)-3\left(\sqrt{x}+1\right)=\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)\)
10, \(-4x^2-4x+10=-\left(4x^2+4x+1\right)+11\)
\(=-\left[\left(2x+1\right)^2-11\right]=-\left(2x+1-\sqrt{11}\right)\left(2x+1+\sqrt{11}\right)\)
11;12 xem lại đề
13, \(-x^3+6xy^2-12xy^2+8y^3=-\left(x^3-6xy^2+12xy^2-8y^3\right)=-\left(x-2y\right)^3\)
Trả lời:
7, \(27x^3+y^3=\left(3x+y\right)\left(9x^2-3xy+y^2\right)\)
8, \(8x^3-\frac{1}{125}y^3=\left(2x-\frac{1}{5}y\right)\left(4x^2+\frac{2}{5}xy+\frac{1}{25}y^2\right)\)
9, \(x-2\sqrt{x}-3\left(ĐK:x\ge0\right)\)
\(=x-3\sqrt{x}+\sqrt{x}-3=\sqrt{x}\left(\sqrt{x}-3\right)+\left(\sqrt{x}-3\right)=\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)\)
10, \(10-4x-4x^2=-\left(4x^2+4x-10\right)=-\left(4x^2+4x+1-11\right)=-\left[\left(2x+1\right)^2-11\right]\)
\(=-\left(2x+1\right)^2+11=-\left[\left(2x+1\right)^2-11\right]=-\left(2x+1-\sqrt{11}\right)\left(2x+1+\sqrt{11}\right)\)
11,sửa đề: \(15x\left(x-3y\right)+20y\left(3y-x\right)=15x\left(x-3y\right)-20y\left(x-3y\right)=5\left(x-3y\right)\left(3x-4y\right)\)
12, \(25x^2-2=\left(5x-\sqrt{2}\right)\left(5x+\sqrt{2}\right)\)
13, sửa đề: \(-x^3+6x^2y-12xy^2+8y^3=-\left(x^3-6x^2y+12xy^2-8y^3\right)=-\left(x-2y\right)^3\)
\(2x^2y^3-\frac{x}{4}-4y^6\)
đây là pt bậc 2 của y^3 , ta đặt y^3=z ta được
\(-\left(4z^2+\frac{2.2xz}{2}+\frac{x^2}{4}\right)+\left(\frac{x^2}{4}-\frac{x}{4}\right)\)
\(-\left(2z+\frac{x}{2}\right)^2+\left(\frac{x^2}{4}-\frac{x}{4}\right)\)
\(-\left\{\left(2x+\frac{x}{2}\right)^2-\left(\frac{x^2}{4}-\frac{x}{4}\right)\right\}\)
\(-\left\{\left(2x+\frac{x}{2}+\sqrt{\frac{x^2}{4}-\frac{x}{4}}\right)\left(2x+\frac{x}{2}-\sqrt{\frac{x^2}{4}-\frac{x}{4}}\right)\right\}\)
a) 3x - 3y
= 3 ( x- y )
b) 2x^2 + 5x^3 + x^2y
= x^2 ( 2+ 5x + y)
c) 14x^2 --21xy^2 + 28x^2y^2
= 7x ( 2x - 3y^2 + 4xy^2)
d) 4x^3 - 14x^2
= x^2 ( 4x - 14 )
e) 5y^10 + 15y^6
= 5y^6 (y^4 + 3 )
f) 9x^2y^2 + 15x^2y -21xy
= 3xy( 3xy + 5x - 7)
g) x( y-1 ) - y ((y-1)
=(y -1) (x-y)
1) \(x^6+1\)
\(=x^6+x^4-x^4+x^2-x^2+1\)
\(=\left(x^6-x^4+x^2\right)+\left(x^4-x^2+1\right)\)
\(=x^2\left(x^4-x^2+1\right)+\left(x^4-x^2+1\right)\)
\(=\left(x^2+1\right)\left(x^4-x^2+1\right)\)
2) \(x^6-y^6\)
\(=\left(x^3+y^3\right)\left(x^3-y^3\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)\left(x-y\right)\left(x^2+xy+y^2\right)\)
A) 7X2 - 7Y2 - 14X + 14Y
= ( 7X2 - 7Y2 ) - ( 14X - 14Y )
= 7( X2 - Y2 ) - 14( X - Y )
= 7( X - Y )( X + Y ) - 14( X - Y )
= 7( X - Y )( X + Y - 14 )
B) X2 - Y2 + 14X + 49
= ( X2 + 14X + 49 ) - Y2
= ( X + 7 )2 - Y2
= ( X - Y + 7 )( X + Y + 7 )
C) X2 - Y2 - X + Y
= ( X2 - Y2 ) - ( X - Y )
= ( X - Y )( X + Y ) - ( X - Y )
= ( X - Y )( X + Y - 1 )
D) X2 + 12Y - Y2 - 36
= X2 - ( Y2 - 12Y + 36 )
= X2 - ( Y - 6 )2
= ( X - Y + 6 )( X + Y - 6 )
E) X3 + X2 - 9X - 9
= ( X3 + X2 ) - ( 9X + 9 )
= X2( X + 1 ) - 9( X + 1 )
= ( X + 1 )( X2 - 9 )
= ( X + 1 )( X - 3 )( X + 3 )
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
cái này có những biểu thức ko dùng được hđt hoặc đặt nhân tử chung =))) anh nghĩ đề em nên thay chữ và thành hoặc
1, \(15x^2+10xy=5x\left(3x+2y\right)\)
2, \(24x-18y+30=6\left(4x-3y+5\right)\)
3, \(2x\left(y-2009\right)+5y\left(y-2009\right)=\left(y-2009\right)\left(2x+5y\right)\)
4, \(35x\left(y-8\right)-14y\left(8-y\right)=\left(y-8\right)\left(35x+14y\right)=7\left(5x+2y\right)\left(y-8\right)\)
5, \(x^2+14x+49=x^2+2.7x+7^2=\left(x+7\right)^2\)
6, \(9x^2-4=\left(3x-2\right)\left(3x+2\right)\)
Trả lời:
1, 15x2 + 10xy = 5x ( 3x + 2y )
2, 24x - 18y + 30 = 6 ( 4x - 3y + 5 )
3, 2x ( y - 2009 ) + 5y ( y - 2009 ) = ( y - 2009 )( 2x + 5y )
4, 35x ( y - 8 ) - 14y ( 8 - y ) = 35x ( y - 8 ) + 14y ( y - 8 ) = ( y - 8 )( 35x + 14y ) = 7 ( y - 8 )( 5x + 2y )
5, x2 + 14x + 49 = ( x + 7 )2
6, 9x2 - 4 = ( 3x - 2 )( 3x + 2 )