\(x^4+x^2y^2+y^2\)
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6 tháng 11 2021
\(1,=x\left(x^2-2x+1-y^2\right)=x\left[\left(x-1\right)^2-y^2\right]=x\left(x-y-1\right)\left(x+y-1\right)\\ 2,=\left(x+y\right)^3\\ 3,=\left(2y-z\right)\left(4x+7y\right)\\ 4,=\left(x+2\right)^2\\ 5,Sửa:x\left(x-2\right)-x+2=0\\ \Leftrightarrow\left(x-2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
12 tháng 10 2021
\(1,\\ a,=4\left(x-2\right)^2+y\left(x-2\right)=\left(4x-8+y\right)\left(x-2\right)\\ b,=3a^2\left(x-y\right)+ab\left(x-y\right)=a\left(3a+b\right)\left(x-y\right)\\ 2,\\ a,=\left(x-y\right)\left[x\left(x-y\right)^2-y-y^2\right]\\ =\left(x-y\right)\left(x^3-2x^2y+xy^2-y-y^2\right)\\ b,=2ax^2\left(x+3\right)+6a\left(x+3\right)\\ =2a\left(x^2+3\right)\left(x+3\right)\\ 3,\\ a,=xy\left(x-y\right)-3\left(x-y\right)=\left(xy-3\right)\left(x-y\right)\\ b,Sửa:3ax^2+3bx^2+ax+bx+5a+5b\\ =3x^2\left(a+b\right)+x\left(a+b\right)+5\left(a+b\right)\\ =\left(3x^2+x+5\right)\left(a+b\right)\\ 4,\\ A=\left(b+3\right)\left(a-b\right)\\ A=\left(1997+3\right)\left(2003-1997\right)=2000\cdot6=12000\\ 5,\\ a,\Leftrightarrow\left(x-2017\right)\left(8x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2017\\x=\dfrac{1}{4}\end{matrix}\right.\\ b,\Leftrightarrow\left(x-1\right)\left(x^2-16\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=4\\x=-4\end{matrix}\right.\)
NM
2
28 tháng 3 2021
Đặt \(A=x^4-2y^4-x^2y^2+x^2+y^2\)
\(\Rightarrow2A=2x^4-4y^4-2x^2y^2+2x^2+2y^2\)
\(\Rightarrow2A=\left(x^4+2x^2+1\right)-\left(y^4-2y^2+1\right)\)\(+\left(x^4-2x^2y^2+y^4\right)-4y^4\)
\(\Rightarrow2A=\left(x^2+1\right)^2-\left(y^2-1\right)^2+\left(x^2-y^2\right)^2-4y^4\)
\(\Rightarrow2A=\left[\left(x^2+1\right)^2-4y^4\right]+\left[\left(x^2-y^2\right)^2-\left(y^2-1\right)^2\right]\)
\(\Rightarrow2A=\left(x^2+1-2y^2\right)\left(x^2+1+2y^2\right)+\)\(\left(x^2-y^2+y^2-1\right)\left(x^2-y^2-y^2+1\right)\)
\(\Rightarrow2A=\left(x^2+1-2y^2\right)\left(x^2+1+2y^2\right)+\)\(\left(x^2-1\right)\left(x^2+1-2y^2\right)\)
\(\Rightarrow2A=\left(x^2+1-2y^2\right)\left(x^2+1+2y^2+x^2-1\right)\)
\(\Rightarrow2A=\left(x^2-2y^2+1\right)\left(2x^2+2y^2\right)\)
\(\Rightarrow2A=2\left(x^2-2y^2+1\right)\left(x^2+y^2\right)\)
\(\Rightarrow A=\left(x^2-y^2+1\right)\left(x^2+y^2\right)\)
28 tháng 3 2021
Nhầm, tớ chốt lại: \(A=\left(x^2-2y^2+1\right)\left(x^2+y^2\right)\), đừng xem cái câu cuối ở tin 1, sai đấy.
TT
0
BT
1
11 tháng 6 2016
\(x^4-2y^4-x^2y^2+x^2+y^2=\left(x^4-y^4\right)-\left(x^2y^2-x^2\right)+\left(y^2-y^4\right)=\left(x^2-y^2\right)\left(x^2+y^2\right)-x^2\left(y^2-1\right)-y^2\left(y^2-1\right)=\left(x^2+y^2\right)\left(x^2-y^2\right)-\left(y^2-1\right)\left(x^2+y^2\right)=\left(x^2+y^2\right)\left(x^2-y^2-y^2+1\right)=\left(x^2+y^2\right)\left(x^2-2y^2+1\right)\)
TH
1
LT
0
L
1
H9
HT.Phong (9A5)
CTVHS
2 tháng 10 2023
\(x^4+1\)
\(=x^4+2x^2+1-2x^2\)
\(=\left(x^2+1\right)^2-\left(x\sqrt{2}\right)^2\)
\(=\left(x^2-x\sqrt{2}+1\right)\left(x^2+x\sqrt{2}+1\right)\)
______
\(4x^4y^4+1\)
\(=4x^4y^4+4x^2y^2+1-4x^2y^2\)
\(=\left(2x^2y^2+1\right)^2-\left(2xy\right)^2\)
\(=\left(2x^2y^2-2xy+1\right)\left(2x^2y^2+2xy+1\right)\)
______
\(x^4+3x^2+4\)
\(=x^4+x^3+2x^2-x^3-x^2-2x+2x^2+2x+4\)
\(=\left(x^4+x^3+2x^2\right)-\left(x^3+x^2+2x\right)+\left(2x^2+2x+4\right)\)
\(=x^2\left(x^2+x+2\right)-x\left(x^2+x+2\right)+2\left(x^2+x+2\right)\)
\(=\left(x^2+x+2\right)\left(x^2-x+2\right)\)
______
\(x^2+3xy+2y^2\)
\(=x^2+xy+2xy+2y^2\)
\(=x\left(x+y\right)+2y\left(x+y\right)\)
\(=\left(x+2y\right)\left(x+y\right)\)
HV
2
27 tháng 8 2016
a,7x(y-4)2-(4-y)3
=7x(4-y)2-(4-y)3
=(4-y)2[7x-(4-y)]
=(4-y)2(7x-4+y)
b, 5x(x-2y)+2(2y-x)2
=5x(x-2y)+2(x-2y)2
=(x-2y)[5x+2(x-2y)]
=(x-2y)(5x+2x-4y)
\(x^4+x^2y^2+y^2\)
\(=x^4+2x^2y^2-x^2y^2+y^2\)
\(=\left(x^4+2x^2y^2+y^2\right)-x^2y^2\)
\(=\left(x^2+y\right)^2-x^2y^2\)
\(=\left(x^2+y-x^2y^2\right)\left(x^2+y+x^2y^2\right)\)