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1 tháng 7 2016

a) \(\Leftrightarrow a^2+b^2+c^2+2ab+2bc+2ca+a^2+b^2+c^2\)

\(\Leftrightarrow a^2+2ab+b^2+b^2+2bc+c^2+a^2+2ac+c^2\)

\(\Leftrightarrow\left(a+b\right)^2+\left(b+c\right)^2+\left(c+a\right)^2\)

        nha

1 tháng 7 2016

bài b) ghi đề sai nha

30 tháng 6 2017

a) (a + b + c)2 + a2 + b2 + c2 

= (a2 + b2 + c2 + 2ab + 2bc + 2ac) + a2 + b2 + c2

= (a2 + b2 + 2ab) + (a2 + c2 + 2ac) + (b2 + c2 + 2bc)

= (a + b)2 + (a + c)2 + (b + c)2

b) 2(a - b)(c - b) + 2(b - a)(c - a) + 2(b - c)(a - c)

= 2ac - 2ab - 2bc + 2b2 + 2bc - 2ab - 2ac + 2a2 + 2ab - 2bc - 2ac + 2c2

= 2b2 - 2ab + 2a2 - 2bc - 2ac + 2c2

= (a2 - 2ab + b2) + (b2 - 2bc + c2) + (c2 - 2ac + a2)

= (a - b)2 + (b - c)2 + (c - a)2

30 tháng 6 2017

a) (a+b+c)2 +a2 +b2 +c2 = a2 +b2 +c2 +2ab+2bc +2ca + a2 +b2 +c2 = 2a2 +2b2 +2c+2ab+2bc+2ac

=(a2 +2ab+b2 ) +(c2 +2bc+b2) +(c2 +2ca +a2 ) =(a+b)2 +(b+c)2 +(c+a)2

                                                                                                  

10 tháng 6 2015

B1)9x4+16y6-24x2y3=(3x2-4y3)2

B2)a)81-x4=(9-x2)(9+x2)=(3-x)(3+x)(9+x2)

b)(2x+y)2-1=(2x+y-1)(2x+y+1)

c)(+y+z)2-(x-y-z)2=(x+y+z-x+y+z)(x+y+z+x-y-z)=(2y+2z)2x=4x(y+z)

B3)

(123+1)(123-1)-36.46

=126-1-(3.4)6

=126-1-126=-1

24 tháng 9 2018

1 : \(\left(a+b+c\right)^2+a^2+b^2+c^2\)

\(=a^2+b^2+c^2+2ab+2bc+2ac+a^2+b^2+c^2\)

\(=\left(a^2+2ab+b^2\right)+\left(b^2+2bc+c^2\right)+\left(c^2+2ac+a^2\right)\)

\(=\left(a+b\right)^2+\left(b+c\right)^2+\left(c+a\right)^2\)

2 : \(2\left(a-b\right)\left(c-b\right)+2\left(b-a\right)\left(c-a\right)+2\left(b-c\right)\left(a-c\right)\)

\(=2\left(ac-bc-ab+b^2\right)+2\left(bc-ac-ab+a^2\right)+2\left(ab-ac-bc+c^2\right)\)

\(=2ac-2bc-2ab+2b^2+2bc-2ac-2ab+2a^2+2ab-2ac-2bc+2c^2\)

\(=2a^2+2b^2+2c^2-2ac-2ab-2bc\)

\(=\left(a^2-2ab+b^2\right)+\left(b^2-2bc+c^2\right)+\left(c^2-2ac+a^2\right)\)

\(=\left(a-b\right)^2+\left(b-c\right)^2+\left(c-a\right)^2\)

24 tháng 9 2018

\(\)\(1.\) \(\left(a+b+c\right)^2+a^2+b^2+c^2\)

\(\Leftrightarrow a^2+b^2+c^2+2ab+2ac+2bc+a^2+b^2+c^2\)

\(\Leftrightarrow\left(a^2+2ab+b^2\right)+\left(a^2+2ac+c^2\right)+\left(b^2+2bc+c^2\right)\)

\(\Leftrightarrow\left(a+b\right)^2+\left(a+c\right)^2+\left(b+c\right)^2\)

\(2.\) \(2\left(a-b\right)\left(c-b\right)+2\left(b-a\right)\left(c-a\right)+2\left(b-c\right)\left(a-c\right)\)

\(\Leftrightarrow2ac-2ab-2bc+2b^2+2bc-2ab-2ac+2a^2+2ab-2bc-2ac+2c^2\)

\(\Leftrightarrow2a^2+2b^2+2c^2-2ab-2ac-2bc\)

Tới đây dùng HĐT

a: \(\left(a+b+c\right)^2+a^2+b^2+c^2\)

\(=2a^2+2b^2+2c^2+2ab+2bc+2ac\)

\(=\left(a^2+2ab+b^2\right)+\left(b^2+2bc+c^2\right)+\left(a^2+2ac+c^2\right)\)

\(=\left(a+b\right)^2+\left(b+c\right)^2+\left(a+c\right)^2\)

b: \(=2\left(a-b\right)\left(c-b\right)-2\left(a-b\right)\left(c-a\right)+2\left(b-c\right)\left(a-c\right)\)

\(=\left(2a-2b\right)\left(c-b-c+a\right)+2\left(b-c\right)\left(a-c\right)\)

\(=\left(2a-2b\right)\left(a-b\right)+2\left(b-c\right)\left(a-c\right)\)

\(=2\left(a^2-2ab+b^2+ab-bc-ac+c^2\right)\)

\(=2\left(a^2+b^2+c^2-ab-bc-ac\right)\)

\(=2a^2+2b^2+2c^2-2ab-2bc-2ac\)

\(=\left(a-b\right)^2+\left(b-c\right)^2+\left(a-c\right)^2\)

29 tháng 9 2022

a) x2+2x+1= (x+1)2

b) 9x2+6xy+y2= (3x+y)2

 

21 tháng 7 2017

a) \(9x^2-6x+1\)

\(=\left(3x\right)^2-2\cdot3\cdot x+1^2\)

\(=\left(3x-1\right)^2\)

b) \(\left(2x+3y\right)^2+2\left(2x+3y\right)+1\)

\(=\left(2x+3y+1\right)^2\)

30 tháng 8 2020

a) 16x2 - 9 

= ( 4x )2 - 32

= ( 4x - 3 )( 4x + 3 )

b) 9a2 - 25b4

= ( 3a )2 - ( 5b2 )2

= ( 3a - 5b2 )( 3a + 5b2 )

c) 81 - y4

= 92 - ( y2 )2

= ( 9 - y2 )( 9 + y2 )

= ( 32 - y2 )( 9 + y2 )

= ( 3 - y )( 3 + y )( 9 + y2 )

d) ( 2x + y )2 - 1

= ( 2x + y )2 - 12

= ( 2x + y - 1 )( 2x + y + 1 )

e) ( x + y + z )2 - ( x - y - z )2

= [ x + y + z - ( x - y - z ) ][ x + y + z + ( x - y - z ) ]

= [ x + y + z - x + y + z ][ x + y + z + x - y - z ]

= [ 2y + 2z ].2x

= 2[ y + z ].2x

= 4x[ y + z ]

31 tháng 7 2018

a)  \(4x^2-4xy+2y^2+2y+1=\left(2x-y\right)^2+\left(y+1\right)^2\)

b)  \(x^2+2x+y^2-4y+5=\left(x+1\right)^2+\left(y-2\right)^2\)

c)  bạn ktra lại đề