2: \(=x^3+3x^2-5x+3x^2+9x-15\)

\(=x^3+6x^2+4x-15\)

Bạn chú thích hơi quá lố :) 

Ta có :( 5x - 3y + 4z ) . ( 5x - 3y - 4z ) \(=\left(5x-3y\right)^2-16z^2\)

\(=25x^2-30xy+9y^2-16z^2\)

Mà x^2=y^2 + z^2 nên ( 5x - 3y + 4z ) . ( 5x - 3y - 4z )\(=25x^2-30xy+9y^2-16\left(x^2-y^2\right)\)

\(=9x^2-30xy+25y^2=\left(3x-5y\right)^2\)

Học tốt !

\(\left(5x-3y+4z\right)\left(5x-3y-4z\right)=\left(3x-5y^2\right)\)

\(\Leftrightarrow\left(5x-3y\right)^2-16z^2-\left(3x-5y\right)^2=0\)

\(\Leftrightarrow\left(5x-3y-3x+5y\right)\left(5x-3y+3x-5y\right)-16z^2=0\)

\(\Leftrightarrow16x^2=16y^2+16z^2\)(luôn đúng)

 \(a^2-3ab+2c=0\)

\(\Leftrightarrow\left(x+y\right)^2-3\left(x+y\right)\left(x^2+y^2\right)+2\left(x^3+y^3\right)=0\)

\(\Leftrightarrow x^2+y^2+2xy-3x^3-3xy^2-3yx^2-3y^3+2y^3+2x^3=0\)

\(\Leftrightarrow\left(x+y\right)^2-\left(x+y\right)^3=0\)

Hình như đề hơi sai nếu là a^3 thì ms đúng chứ

mk chỉ góp ý thui tại làm mãi ko ra

hhihihihi

\(\text{- ( 2789 _ 435 ) + ( 1789 _ 1435 )}\)

\(=-2789+435+1789-1435\)

\(=\left(-2789+1789\right)+\left(435-1435\right)\)

\(=-1000+-1000\)

\(=-2000\)

\(=-\left(-2010\right)+36.41-36.\left(-59\right)\)

\(=2010+36.\left(41+59\right)\)

\(=2010+36.100\)

\(=2010+3600\)

\(=5610\)

\(-75.\left(18-65\right)-65.\left(75-18\right)\)

\(=-75.18+75.65-65.75+65.18\)

\(=18.\left(-75+65\right)+75.\left(65-65\right)\)

\(=18.\left(-10\right)+75.0\)

\(=-180\)

\(-15:x=3\)

\(x=-15:3\)

\(x=-5\)

\(-3x+8=7\)

\(-3x=-1\)

\(x=\frac{1}{3}\)

\(\left(x-6\right).\left(7-x\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x-6=0\\7-x=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=6\\x=7\end{cases}}}\)

\(\Rightarrow x\in\left\{6;7\right\}\)

\(2.\left(x-3\right)-3.\left(x-5\right)=4.\left(3-x\right)-18\)

\(2x-6-3x+15=12-4x-18\)

\(2x-3x+4x=12-18-15+6\)

\(3x=-15\)

\(\Rightarrow x=-5\)

\(-a.\left(c-d\right)-d.\left(a+c\right)=-c.\left(a+d\right)\)

\(-a.c+a.d-d.a+-d.c=-c.\left(a+d\right)\)

\(-c.\left(a+d\right)+a.\left(d-d\right)=-c.\left(a+d\right)\)

\(-c.\left(a+d\right)+a.0=-c.\left(a+d\right)\)

\(\Rightarrow-c.\left(a+d\right)=-c.\left(a+d\right)\)

(3a+2).(2a–1)+(3–a).(6a+2)–17.(a–1)

=6a²−3a+4a−2+18a+6−6a²−2a−17a+17

=(6a²−6a²)+(−3a+4a+18a−2a−17a)+(17−2+6)

=0+0+21

=21

học tốt

Ta cần c/m: \(\dfrac{a+b}{2}\ge\sqrt{ab}\left(1\right)\) (a;b ≥ 0)

Thật vậy:

\(\left(1\right)\Leftrightarrow\left(\dfrac{a+b}{2}\right)^2\ge ab\\ \Leftrightarrow\dfrac{a^2+2ab+b^2}{4}\ge ab\\ \Leftrightarrow a^2+2ab+b^2\ge4ab\\ \Leftrightarrow a^2-2ab+b^2\ge0\\ \Leftrightarrow\left(a-b\right)^2\ge0\left(\text{luôn đúng }\forall a;b\ge0\right)\)

Vậy BĐT Cô-si cho 2 số không âm được c/m.

a,

 C1: (a - b + c)² =  (a - b + c) (a - b + c)

                          = a (a - b + c) - b (a - b + c) +c (a - b + c)

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

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

C2: (a - b + c)² = [ (a - b) + c ]²

                         = (a - b)² + 2c (a - b) + c²

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

b,

C1: (a + b + c)(a + b - c) = a (a + b - c) + b (a + b - c) + c (a + b - c)

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

                                        = a² + 2ab + b² - c² 

C2: (a + b + c)(a + b - c) =  [ (a + b) + c ] [ ( a+ b) - c ] 

                                        = (a + b)² - c² 

                                        = a² + 2ab + b² - c²

hok tốt ~

( a + b ) _ ( b _ a ) + c = 2a + c

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

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

\(2a+0+c=2a+c\)

\(2a+c=2a+c\Rightarrowđpcm\)

- ( a + b _ c ) + ( a _ b _c ) = - 2b

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

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

\(0-2b+0=-2b\)

\(-2b=-2b\Rightarrowđpcm\)

a nhân ( b+ c ) _ a nhân ( b + d ) = a nhân ( c _ d )

\(ab+ac-ab+ad=a.\left(c-d\right)\)

\(a.\left(b+c-b+d\right)=a.\left(c-d\right)\)

\(a.\left(c-d\right)=a.\left(c-d\right)\Rightarrowđpcm\)

a nhân ( b _ c ) + a nhân ( d + c ) = a nhân ( b + d )

\(ab-ac+ad+ac=a.\left(b+d\right)\)

\(a.\left(b-c+d+c\right)=a.\left(b+d\right)\)

\(a.\left(b+d\right)=a.\left(b+d\right)\)

chúc bạn học tốt!!!

( a _ b + c ) _ ( a+ c ) = - b

\(a-b-c-a-=-b\)

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

\(0-c-b=-b\)

\(-b=-b\Rightarrowđpcm\)

#maianhhomework

Chọn đáp án B

a: =(x+y)^3+z^3-3xy(x+y)-3xyz

=(x+y+z)(x^2+2xy+y^2-xz-yz+z^2)-3xy(x+y+z)

=(x+y+z)(x^2+y^2+z^2-xy-xz-yz)

b: a+b+c<>0

A=(a+b+c)^3-a^3-b^3-c^3/a+b+c

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

=a^2+b^2+c^2-ab-ac-bc

=1/2[a^2-2ab+b^2+b^2-2bc+c^2+a^2-2ac+c^2]

=1/2[(a-b)^2+(b-c)^2+(a-c)^2]>=0