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a: \(=3x^3-2x^2+5x\)
b: \(=x^3-2x^2+3x+6x^2-12x+18\)
\(=x^3+4x^2-9x+18\)
c: \(=2x^2-6xy+6xy-15y^2=2x^2-15y^2\)
d: \(=\left(x+3\right)\left(x^2-9\right)-x^3+27\)
\(=x^3-9x+3x^2-27-x^3+27=3x^2-9x\)
a) \(10x^2-29x+10\)
\(=10x^2-4x-25x+10\)
\(=2x\left(5x-2\right)-5\left(5x-2\right)\)
\(=\left(5x-2\right)\left(2x-5\right)\)
a) \(A=x^2-2x+2=\left(x^2-2x+1\right)+1=\left(x-1\right)^2+1\ge1\)
Vậy GTNN của A là 1 khi x = 1
b) \(B=x^2-4x+y^2-8y+6\)
\(B=\left(x^2-4x+4\right)+\left(y^2-8y+16\right)-14\)
\(B=\left(x-2\right)^2+\left(y-4\right)^2-14\ge-14\)
Vậy GTNN của B là -14 khi x = 2; y = 4
a, A = x2 - 2x + 2
=(x2 -2x + 1) +1
=(x-1)2 + 1 >= 1
Dấu bằng xảy ra <=> (x-1)2 = 0
<=> x - 1 = 0
<=> x = 1
Vậy...
b, B = x2 - 4x + y2- 8y + 6
B =(x2 - 4x + 4) + (y2- 8y + 16) - 14
B =(x - 2)2 + (y - 4)2 -14 >= -14
Dấu bằng xảy ra + <=> x - 2 = 0
<=> x = 2
+ <=> y - 4 = 0
<=> y = 4
Vậy ...
Bài này dài vc sao làm hết dc.
a) \(3y^2\left(2y-1\right)+y-y\left(1-y+y^2\right)-y^2+y \)
= \(6y^3-3y^2+y-y+y^2-y^3-y^2+y\)
= \(5y^3-3y^2+y\)
b)\(25x-4\left(3x-1\right)+\left(5-2x\right)7\)
= \(25x-12x+4+35-14x\)
= \(-x+39\)
c) \(11x-2\left(10x-1\right)-\left(4x-1\right)\left(-2\right)\)
= \(11x-\left(20x-2\right)-\left(-8x+2\right)\)
= \(11x-20x+2+8x-2\)
= \(-x\)
d) \(\left(\frac{1}{2x}\right)3-x\left(1-2x-\frac{1}{8x^2}\right)-x\left(x+\frac{1}{2}\right)\)
= \(\frac{3}{2x}-x+2x^2+\frac{x}{8x^2}-x^2-\frac{x}{2}\)
= \(\left(\frac{3}{2x}+\frac{1}{8x}-\frac{x}{2}\right)+x^2-x\)
= \(\left(\frac{12+1-4x^2}{8x}\right)+x^2-x\)
= \(\frac{13-4x^2}{8x}+\frac{8x^3}{8x}-\frac{8x^2}{8x}\)
= \(\frac{13-4x^2+8x^3-8x^2}{8x}\)
= \(\frac{8x^3-12x^2+13}{8x}\)
= x2 - \(\frac{3}{2}\)+\(\frac{13}{8x}\)
e) \(12\left(2-3x\right)+35x-\left(x+1\right)\left(-5\right)\)
= \(24-36x+35x-\left(-5x-5\right)\)
= \(24-36x+35x+5x+5\)
= 4x + 29
a.[ (2x+3y)2- 4(2x+3y)+4] - 22
= (2x+3y-2)2-22
= (2x+3y)(2x+3y-4)
b. tách ra trừ x3 và y3 rồi đặt nhân tử chung
c. làm theo hằng đẳng thức a2-b2
d. tách ra rồi làm
e. thêm bớt
f. thêm bớt 4x2
a) A = 4x2 + 4x +11
=> (2x)2+2.2x+1+11-1
=> (2x+1)2+10
do (2x+1)2 \(\dfrac{>}{ }\) 0 vs mọi x
(2x+1)2 +10 \(\dfrac{>}{ }\)10 vs mọi x
GTNNA=10 khi
2x+1=0
=>x=\(\dfrac{-1}{2}\)
a)\(A=4x^2+4x+11\)
\(\Leftrightarrow A=4x^2+4x+1+10\)
\(\Leftrightarrow A=\left(2x+1\right)^2+10\)
Vì \(\left(2x+1\right)^2\ge0\)
Nên \(\left(2x+1\right)^2+10\ge10\)
Vậy GTNN của A=10 khi \(2x+1=0\Leftrightarrow x=\dfrac{-1}{2}\)
b) \(B=2x-2x^2-5\)
\(\Leftrightarrow B=-2x^2+2x-5\)
\(\Leftrightarrow B=-2x^2+2x-\dfrac{1}{2}-\dfrac{9}{2}\)
\(\Leftrightarrow B=-\left(2x^2-2x+\dfrac{1}{2}\right)-\dfrac{9}{2}\)
\(\Leftrightarrow B=-2\left(x^2-x+\dfrac{1}{4}\right)-\dfrac{9}{2}\)
\(\Leftrightarrow B=-2\left(x^2-2.x\dfrac{1}{2}+\dfrac{1}{4}\right)-\dfrac{9}{2}\)
\(\Leftrightarrow B=-2\left(x-\dfrac{1}{2}\right)^2-\dfrac{9}{2}\)
Vì \(\left(x-\dfrac{1}{2}\right)^2\ge0\)
Do đó \(-\left(x-\dfrac{1}{2}\right)^2\le0\)
Nên \(-\left(x-\dfrac{1}{2}\right)^2-\dfrac{9}{2}\le\dfrac{-9}{2}\)
Vậy GTLN của \(B=\dfrac{-9}{2}\) khi \(x-\dfrac{1}{2}=0\Leftrightarrow x=\dfrac{1}{2}\)
c) \(C=4x^2-12x\)
\(\Leftrightarrow C=4x^2-12x+9-9\)
\(\Leftrightarrow C=\left(4x^2-12x+9\right)-9\)
\(\Leftrightarrow C=\left(2x-3\right)^2-9\)
Vì \(\left(2x-3\right)^2\ge0\)
Nên \(\left(2x-3\right)^2-9\ge-9\)
Vậy GTNN của \(C=-9\) khi \(2x-3=0\Leftrightarrow x=\dfrac{3}{2}\)
d) \(D=5-x^2+2x-4y^2-4y\)
\(\Leftrightarrow D=7-1-1-x^2+2x-4y^2-4y\)
\(\Leftrightarrow D=-x^2+2x-1-4y^2-4y-1+7\)
\(\Leftrightarrow D=-\left(x^2-2x+1\right)-\left(4y^2+4y+1\right)+7\)
\(\Leftrightarrow D=-\left(x-1\right)^2-\left(2y+1\right)^2+7\)
Vậy GTLN của \(D=7\) khi \(\left\{{}\begin{matrix}x-1=0\Leftrightarrow x=1\\2y+1=0\Leftrightarrow y=\dfrac{-1}{2}\end{matrix}\right.\)
a) 2x2.(5x3-4x2y-7xy +1) =10x5-8x4y-14x3y+2x2 b) (5x -2y)(x2 -xy +1) =5x3-5x2y+5x-2x2y+2xy2-2y =5x3-7x2y+2xy2+5x-2y c) (\(\dfrac{1}{2}\)x -1)(2x -3) =x2-\(\dfrac{3}{2}\)x-2x+3 =x2-\(\dfrac{7}{2}\)x+3 d) (x +3y)2 =x2+6xy+9y2 e) (3x -2y)2 =9x2-12xy+4y2 g) (\(\dfrac{1}{4}\)x - 3y)(\(\dfrac{1}{4}\)x +3y) =\(\dfrac{1}{16}\)x2-9y2 f) (2x +3)3 =8x3+36x2+54x+27 h) (3 -2y)3 =27-54y+36y2-8y3
\(A=4x^2+12x+9\\ B=121x^2-44x+4\\ C=16x^2-9y^2\\ D=4x^2+20x+25\\ E=x^2-12x+36\)
a) (2x)^2 +12x+9
b)(11x)^2 -44x +4
c)48x^2y -36xy^2
d)4x^2 +20x +25
e)x^2 -12x +36