P =( x²  + y² +1 - 2x - 2y +2xy ) + 2 (x² + 2xy + y² ) -  101

P=(x + y   1)² +2(x + y)²   101

P=(5 -1)² +2.5² -101                          (vì x+y=5)

P=    35

\(A=3x^2-2x+3y^2-2y+6xy-100\)

\(=\left(3x^2+6xy+3y^2\right)-2x-2y-100\)

\(=3\left(x+y\right)^2-2\left(x+y\right)-100\)

\(=3.5^2-2.5-100\)

\(=75-10-100\)

\(=-35\)

3x²-2x+3y²-2y+6xy-100=(3x²+3y²+6xy)-(2x+2y)-100

=3(x²+y²+2xy)-2(x+y)-100=3(x+y)²-2(x+y)-100

Thay x+y=5 vào biểu thức ta có

3.5²-2.5-100=75-10-100=-35

A=3(x2+2xy+y2)-2(x+y)-100=3(x+y)2-2.5-100=3.52-110=-35    

B=x3+3x2y+3xy2+y3-2(x2+2xy+y2)+3(x+y)+10=(x+y)3-2(x+y)2+3.5+10=53-2.52+25=100

trả lời:

A=3(x2+2xy+y2)-2(x+y)-100

=3(x+y)2-2.5-100

=3.52-110

=-35

B=x3+3x2y+3xy2+y3-2(x2+2xy+y2)+3(x+y)+10

 =(x+y)3-2(x+y)2+3.5+10

 =53-2.52+25

 =100

học tốt

câu a sai đề, như thế này nè:

A = x³ + y³ - 2x² - 2y² + 3xy (x + y) - 4xy + 3(x + y) +10 

a,A = x³ + y³ - 2x² - 2y² + 3xy (x + y) - 4xy + 3(x + y) +10

A = x³ + y³ - 2x² - 2y² + 3x²y + 3xy² - 4xy + 3x + 3y +10

A = (x³ + 3x²y + 3xy² + y³) - (2x² + 4xy + 2y²) + (3x + 3y) +10

A = (x + y)³ - 2 (x + y)² +3(x + y) +10

Thay x + y = 5 ta được:

A = 5³ - 2. 5² + 3.5 +10 = 100

 b, B = 3x² - 2x + 3y² - 2y + 6xy - 100  

B = (3x² + 3y² + 6xy ) - (2x + 2y) -100

B = 3(x + y)² - 2(x + y) - 100

Thay x + y = 5 ta được:

B = 3.5² - 2.5-100 = -35

\(a,P=3x^2-2x+3y^2-2y+6xy-100\)

\(P=3\left(x^2+y^2\right)-\left[2\left(x+y\right)\right]+6xy-100\)

\(P=3\left(x^2+y^2+2xy-2xy\right)-2.5+6xy-100\)

\(P=3\left(x+y\right)^2-6xy-10+6xy-100\)

\(P=3.25-10-100\)

\(P=-35\)

\(b,Q=x^3+y^3-2x^2-2y^2+3xy\left(x+y\right)-4xy+3\left(x+y\right)+10\)

\(Q=\left(x+y\right)\left(x^2-xy+y^2\right)-2\left(x^2+y^2+2xy-2xy\right)+3xy.5-4xy+3.5+10\)\(Q=5.\left(x^2+y^2+2xy-3xy\right)-2\left(x+y\right)^2+4xy+15xy-4xy+25\)

\(Q=5.5-15xy-2.25+15xy+25\)

\(Q=25-50+25=0\)

a) P= 3x² -2x + 3y²-2y + 6xy -100

= (3x²+ 3y² + 6xy) - 2(x+y) -100

=3(x² + y² +2xy) - 2(x+y) -100

=3(x+y)² - 2(x+y) -100

=3 . 5² -2 .5 -100

=35

b) Q=x³ + y³ -2x² -2y² + 3xy (x+y) -4xy + 3(x+y) + 10

=(x³ +y³) + 3xy (x+y) + 3(x+y) -4xy -2x² -2y² + 10

=(x+y) (x² -xy +y² ) + 3xy (x+y) + 3 (x+y) - 2 (2xy + x² +y² ) + 10

=(x+y) (x² -xy +y² + 3xy ) + 3(x+y) -2 (2xy + x² + y² ) + 10

=(x+y) (x² +2xy +y² ) + 3(x+y) - 2(x+y)² + 10

= (x+y)³ + 3(x+y) - 2 (x+y)² + 10

=5³ + 3.5 -2. 5²+ 10

=100

a)

\(P=3x^2-2x+3y^2-2y+6xy-100\)

\(P=\left(3x^2+3xy\right)+\left(3y^2+3xy\right)-\left(2x+2y\right)-100\)

\(P=3x\left(x+y\right)+3y\left(x+y\right)-2\left(x+y\right)-100\)

\(P=\left(x+y\right)\left(3x+3y-2\right)-100\)

Vì x + y = 5 (1)

=> 3(x + y) = 15

=> 3x + 3y = 15 (2)

Thay (1), (2) vào P ta được:

\(P=5\left(15-2\right)-100\)

\(P=5.13-100\)

\(P=-35\)

Bài 1:
a) (2x - y) + (2x - y) + (2x - y) + 3y
= 3(2x - y) + 3y
= 3(2x - y + 3y)
= 3(2x + 2y)
= 3.2(x + y)
= 6(x + y)

b) (x + 2y) + (x - 2y) + (8x - 3y)
= x + 2y + x - 2y + 8x - 3y
= 9x - 3y
= 3(3x - y)

c) (x + 2y) - 2(x - 2y) - (2x - 3y)
= x + 2y - 2x + 4y - 2x + 3y
= 9y - 3x
= 3(3y - x)

Bài 2:
M + 2(x² - 4y²) + Q = 6x² - 4xy + 5y² + P
M + 2x² - 8y²   -3x² + 7xy - 2y² = 6x² - 4xy + 5y² + 9x² - 6xy + 3y²
M + 2x² - 3x² - 6x² - 9x² - 8y² - 2y² - 5y² - 3y² + 7xy + 4xy + 6xy = 0
M - 16x² - 18y² + 17xy = 0
M = 16x² + 18y² - 17xy

Ta có : \(C=3x^2-2x+3y^2-2y+6xy-100\)

= \(\left(3x^2+3y^2+6xy\right)-\left(2x+2y\right)-100\)

=\(3\left(x+y\right)^2-2\left(x+y\right)-100\)

=\(3\cdot5^2-2\cdot5-100=-35\)

cảm ơn nhìu nhìu nhìu nha ^.^