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A) 2x2(1-3x)+6x3
=2x2*(1-3x)+2x2*3x
=2x2*(1-3x+3x)
=2x2
B) (x-y)2+(x+y)2+2(x-y)(x+y)
=2(x2-y2)+x2+2xy+y2+x2-2xy+y2
=2x2-2y2+x2+2xy+y2+x2-2xy+y2
=4x2
\(A=1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{2017}}\)
\(\Rightarrow2A=2+1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{2016}}\)
\(\Rightarrow2A-A=\left(2+1+\dfrac{1}{2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2016}}\right)\)
\(-\left(1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{2017}}\right)\)
\(\Rightarrow A=2-\dfrac{1}{2^{2017}}=\dfrac{2^{2018}-1}{2^{2017}}\)
\(A=1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{2017}}\)
\(2A=\left(2+1+\dfrac{1}{2}+...+\dfrac{1}{2^{2016}}\right)\)
\(2A-A=\left(2+1+\dfrac{1}{2}+...+\dfrac{1}{2^{2016}}\right)-\left(1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{2017}}\right)\)
\(A=2-2^{2017}\)
\(=\left(\left(x+1\right)^2-\left(x-1\right)^2\right)-3\left(x^2-1\right)\)
\(=4x-3x^2+1\)
Rut gon bieu thuc ( 2x like )
a)28^15 . 3^17
_____________
84^16
b) 3^10 + 6^2
________________
5.3^8 + 20
+) Nếu x > 0
B = 3 . ( -1 ) - 2 . ( x + 3 )
B = -3 - 2x - 6
B = -9 - 2x
+) Nếu x < 0
B = 3 . ( - 1 ) - 2 . ( -x - 3 )
B = -3 + 2x + 3
B = 2x
2ax^2-a(1+2x^2)-[a-x(x+a)]
=2ax2-2ax2+a+x2-ax+a
=(2ax2-2ax2)-(a+a)+ax+x2
=0-2a+ax+x2
=x2+ax-2a