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N = 8x3 – 12x2y + 6xy2 – y3
= (2x)3 – 3(2x)2y + 3.2xy2 – y3 (Hằng đẳng thức (5))
= (2x – y)3
Thay x = 6, y = - 8 ta được:
N = (2.6 – (-8))3 = 203 = 8000
M = x2 + 4y2 – 4xy
= x2 – 2.x.2y + (2y)2 (Hằng đẳng thức (2))
= (x – 2y)2
Thay x = 18, y = 4 ta được:
M = (18 – 2.4)2 = 102 = 100
Ta có
A = 8 x 3 – 12 x 2 y + 6 x y 2 – y 3 + 12 x 2 – 12 x y + 3 y 2 + 6 x – 3 y + 11 = ( 2 x ) 3 – 3 . ( 2 x ) 2 . y + 3 . 2 x . y - y 3 + 3 ( 4 x 2 – 4 x y + y 2 ) + 3 ( 2 x – y ) + 11 = ( 2 x – y ) 3 + 3 ( 2 x – y ) 2 + 3 ( 2 x – y ) + 1 + 10 = ( 2 x – y + 1 ) 3 + 10
Thay 2x – y = 9 vào A = ( 2 x – y + 1 ) 3 + 10 ta được
A = ( 9 + 1 ) 3 + 10 = 1010
Vậy A = 1010
Đáp án cần chọn là: C
a: \(x^2+4x+4=x^2+2\cdot x\cdot2+2^2=\left(x+2\right)^2\)
b: \(4x^2-4x+1=\left(2x\right)^2-2\cdot2x\cdot1+1^2=\left(2x-1\right)^2\)
c: \(2x-1-x^2\)
\(=-\left(x^2-2x+1\right)=-\left(x-1\right)^2\)
d: \(x^2+x+\dfrac{1}{4}=x^2+2\cdot x\cdot\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2=\left(x+\dfrac{1}{2}\right)^2\)
e: \(9-x^2=3^2-x^2=\left(3-x\right)\left(3+x\right)\)
g: \(\left(x+5\right)^2-4x^2=\left(x+5+2x\right)\left(x+5-2x\right)\)
\(=\left(5-x\right)\left(5+3x\right)\)
h: \(\left(x+1\right)^2-\left(2x-1\right)^2\)
\(=\left(x+1+2x-1\right)\left(x+1-2x+1\right)\)
\(=3x\left(-x+2\right)\)
i: \(=x^2y^2-4xy+4-3\)
\(=\left(xy-2\right)^2-3=\left(xy-2-\sqrt{3}\right)\left(xy-2+\sqrt{3}\right)\)
k: \(=y^2-\left(x-1\right)^2\)
\(=\left(y-x+1\right)\left(y+x-1\right)\)
l: \(=x^3+3\cdot x^2\cdot2+3\cdot x\cdot2^2+2^3=\left(x+2\right)^3\)
m: \(=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot y+3\cdot2x\cdot y^2-y^3=\left(2x-y\right)^3\)
Bài 1:
$2xy=(x+y)^2-(x^2+y^2)=4^2-10=6\Rightarrow xy=3$
$M=x^6+y^6=(x^3+y^3)^2-2x^3y^3$
$=[(x+y)^3-3xy(x+y)]^2-2(xy)^3=(4^3-3.3.4)^2-2.3^3=730$
Bài 2:
$8x^3-32y-32x^2y+8x=0$
$\Leftrightarrow (8x^3+8x)-(32y+32x^2y)=0$
$\Leftrightarrow 8x(x^2+1)-32y(1+x^2)=0$
$\Leftrightarrow (8x-32y)(x^2+1)=0$
$\Rightarrow 8x-32y=0$ (do $x^2+1>0$ với mọi $x$)
$\Leftrightarrow x=4y$
Khi đó:
$M=\frac{3.4y+2y}{3.4y-2y}=\frac{14y}{10y}=\frac{14}{10}=\frac{7}{5}$
a.
\(M=x^2+4y^2-4xy=\left(x-2y\right)^2=\left(18-4.2\right)^2=10^2=100\)
b.
\(N=\left(2x\right)^3-3.\left(2x\right)^2.y-3.2x.y^2-y^3=\left(2x-y\right)^3=\left(2.6-\left(-8\right)\right)^3\)
\(=20^3=8000\)