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a, \(x^3-3x^2+3x-1=\left(x-1\right)^3\)
b, \(1-9x+27x^2-27x^3=-\left(3x-1\right)^3\)
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Bài 1:
\(a,27x^3+27x^2+9x+1\)
\(=\left(3x\right)^3+3.\left(3x\right)^2.1+3.3x.1^2+1^3\)
\(=\left(3x+1\right)^3\)
\(b,x^3+3\sqrt{2}x^2y+6xy^2+2\sqrt{2}y^3\)
\(=x^3+3.x^2.\sqrt{2}y+3.x.\left(\sqrt{2}y\right)^2+\left(\sqrt{2}y\right)^3\)
\(=\left(x+\sqrt{2}y\right)^3\)
Bài 2:
\(a,x^3+9x^2+27x+27=0\)
\(\Leftrightarrow\left(x+3\right)^3=0\)
\(\Leftrightarrow x+3=0\Leftrightarrow x=-3\)
\(b,\left(x+1\right)^3-x\left(x-2\right)^2+x-1=0\)
\(\Leftrightarrow x^3+3x^2+3x+1-x^3-4x^2+4x+x-1=0\)
\(\Leftrightarrow-x^2+8x=0\)
\(\Leftrightarrow-x\left(x-8\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=8\end{matrix}\right.\)
1)
a) = (3x+1)3
b) (x+\(\sqrt{2}\) )3
2)
a)\(x^3+9x^2+27x+27=0\\ \left(x+3\right)^3=0\\ =>x=-3\)
b) Bài cuối bạn tự làm nhé! Mình mắc học bài
# Chúc bạn học tốt !
Lời giải:
a) $x^3+3x^2y+x+3xy^2+y+y^3$
$=(x^3+3x^2y+3xy^2+y^3)+(x+y)$
$=(x+y)^3+(x+y)=(x+y)[(x+y)^2+1]$
b) $x^3+y(1-3x^2)+x(3y^2-1)-y^3$
$=(x^3-3x^2y+3xy^2-y^3)-(x-y)$
$=(x-y)^3-(x-y)=(x-y)[(x-y)^2-1]=(x-y)(x-y-1)(x-y+1)$
c)
$27x^3+27x^2+9x+1=(3x+1)^3$
d)
$x(x+1)^2+x(x-5)-5(x+1)^2$
$=x(x+1)^2-5(x+1)^2+x(x-5)$
$=(x-5)(x+1)^2+x(x-5)=(x-5)[(x+1)^2+x]$
$=(x-5)(x^2+3x+2)=(x-5)(x+1)(x+2)$
a) Ta có: \(x^2+2x+1\)
\(=x^2+2\cdot x\cdot1+1^2\)
\(=\left(x+1\right)^2\)
b) Ta có: \(1-2y+y^2\)
\(=y^2-2\cdot y\cdot1+1^2\)
\(=\left(y-1\right)^2\)
c) Ta có: \(x^3-3x^2+3x-1\)
\(=x^3-x^2-2x^2+2x+x-1\)
\(=x^2\left(x-1\right)-2x\left(x-1\right)+\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-2x+1\right)\)
\(=\left(x-1\right)^3\)
d) Ta có: \(27+27x+9x^2+x^3\)
\(=x^3+3x^2+6x^2+18x+9x+27\)
\(=x^2\left(x+3\right)+6x\left(x+3\right)+9\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2+6x+9\right)\)
\(=\left(x+3\right)^3\)
e) Ta có: \(8-125x^3\)
\(=2^3-\left(5x\right)^3\)
\(=\left(2-5x\right)\left(4+10x+25x^2\right)\)
f) Ta có: \(64x^3+\frac{1}{8}\)
\(=\left(4x\right)^3+\left(\frac{1}{2}\right)^3\)
\(=\left(4x+\frac{1}{2}\right)\left(16x^2-2x+\frac{1}{4}\right)\)
g) Ta có: \(1-x^2y^4\)
\(=1^2-\left(xy^2\right)^2\)
\(=\left(1-xy^2\right)\left(1+xy^2\right)\)
a) \(x^2+2x+1=x^2+2x.1+1^2=\left(x+1\right)^2\)
b) \(1-2y+y^2=1^2-2y.1+y^2=\left(1-y\right)^2\)
c) \(x^3-3x^2+3x-1=\left(x-1\right)^3\)
d) \(27+27x+9x^2+x^3=3^3+3.3^2x+3.3x^2+x^3=\left(3+x\right)^3\)
e) \(8-125x^3=2^3-\left(5x\right)^3=\left(2-5x\right)\left[2^2+2.5x+\left(5x\right)^2\right]=\left(2-5x\right)\left(4+10x+25x^2\right)\)
f) \(64x^3+\frac{1}{8}=\left(4x\right)^3+\left(\frac{1}{2}\right)^3=\left(4x+\frac{1}{2}\right)\left[\left(4x\right)^2-4x.\frac{1}{2}+\left(\frac{1}{2}\right)^2\right]=\left(4x+\frac{1}{2}\right)\left(16x^2-2x+\frac{1}{4}\right)\)
Ko chắc ạ!
a. x3 - 3x2 + 3x - 1
= (x-1)3
b. (x+y)2 - 4x2
=(x+y-4x)(x+y+4x)
c. 27x3 + 1/8
= (3x)3 +(1/2)3
=(3x+ 1/2) (9x - 3x.1/2 - 1/4)
d. ( x+y)3 - (x-y)3
= [(x+y)-(x-y)] [(x+y)2 + (x+y)(x-y) + (x-y)2]
=(x+y-x+y)[x2+2xy+y2+x2-y2+x2-2xy+y2)
=2y . (3x2+y2)
Mấy câu này ko biết đúng hay sai :{
\(27x^3-27x^2+9x-1=\left(3x\right)^3-3.\left(3x^2\right).1+3.3x.1+1^3=\left(3x-1\right)^3\)
b) không hiểu đề
Tham khảo~
b)3x^2-18x+27=3x^2-9x-9x+27=3x*(x-3)-9*(x-3)=(x-3)*(3x-9)=(x-3)*3*(x-3)=3*(x-3)^2
c)x^3-4x^2-12x+27=(x+3)*(x^2-3x+9-4)=(x+3)*(x^2-3x+5)
d)27x^3-1/27=(3x-1/3)*(9x^2-x+1/9) (hang dt)
con a) voi e) mk chiu
a) x3 - 125 = x3 - 53 = ( x - 5 )( x2 + 5x + 25 )
b) a3 + 27 = a3 + 33 = ( a + 3 )( a2 - 3a + 9 )
c) -64 + 1/8x3 = ( 1/2x )3 - 43 = ( 1/2x - 4 )( 1/4x2 + 2x + 16 )
d) 0, 001 - 1000x3 = ( 1/10 )3 - ( 10x )3 = ( 1/10 - 10x )( 1/100 + x + 100x2 )
e) ( x + 1 )3 - ( 2 - x )3 = [ ( x + 1 ) - ( 2 - x ) ][ ( x + 1 )2 + ( x + 1 )( 2 - x ) + ( 2 - x )2 ]
= ( x + 1 - 2 + x )( x2 + 2x + 1 - x2 + x + 2 + 4 - 4x + x2 )
= ( 2x - 1 )( x2 - x + 7 )
f) 1/125 + ( x - 1/5 )3 = ( 1/5 )3 + ( x - 1/5 )3
= [ 1/5 + ( x - 1/5 ) ][ 1/25 - 1/5( x - 1/5 ) + ( x - 1/5 )2 ]
= ( 1/5 + x - 1/5 )( 1/25 - 1/5x + 1/25 + x2 - 2/5x + 1/25 )
= x( x2 - 3/5x + 3/25 )
Bài làm :
\(a)x^3-125=x^3-5^3=\left(x-5\right)\left(x^2+5x+25\right)\)
\(b)a^3+27=a^3+3^3=\left(a+3\right)\left(a^2-3a+9\right)\)
a) (3x-1)3 Xem lại đề câu a là -1
b) (x-1)3
c) (1/3 + x)(1/9 -x.1/3 +x2)
d) (0,1-10x)(0,01 + x +100x2)