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a) 11x + 11y + x2 + xy
= 11.(x+y) + x.(x+y)
= (x+y).(11+x)
b) 255 + x2 - 4xy + y2
= 255 + 2xy + x2 -2xy + y2
= 255 + 2xy + (x-y)2
...
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1. a) 2x2 - 8x
= 2x(x - 4)
b) x2 - xy + x - y
= x(x - y) + (x - y)
= (x + 1)(x - y)
2. a) Ta có M = x2 + 5y2 + 4xy + 4y + 11
= (x2 + 4xy + 4y2) + (y2 + 4y + 4) + 7
= (x + 2y)2 + (y + 2)2 + 7 \(\ge7\forall x;y\)
Dấu "=" xảy ra <=> \(\hept{\begin{cases}x+2y=0\\y+2=0\end{cases}}\Rightarrow\hept{\begin{cases}x=-2y\\y=-2\end{cases}}\Rightarrow\hept{\begin{cases}x=4\\y=-2\end{cases}}\)
Vậy Min M = 7 <=> x = 4 ; y = -2
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= \(-\left(x^2+4xy+4y^2\right)\)
= \(-\left(x+2y\right)^2\)
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a) x3-2x2-x+2
=x(x2-1)+2(-x2+1)
=x(x2-1)-2(x2-1)
=(x2-1)(x-2)
b)
x2+6x-y2+9
=x2+6x+9-y2
=(x+3)2-y2
=(x+3-y)(x+3+y)
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a.\(x^2-y^2-2y-1\)
\(=x^2-\left(y^2+2y+1\right)\)
\(=x^2-\left(y+1\right)^2\)
\(=\left(x-y-1\right)\left(x+y+1\right)\)
b.\(4x^2-4xy-81+y^2\)
\(=\left(4x^2-4xy+y^2\right)-9^2\)
\(=\left(2x-y\right)^2-9^2\)
\(=\left(2x-y-9\right)\left(2x-y+9\right)\)
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=x(9x^2-4y^2+4y-1)
=x(9x^2-(2y-1)^2)
=x(3x-2y+1)(3x+2y-1)
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