\(A=2x^2+4xy+2y^2-3x-3y+8\)

\(=2\left(x^2+2xy+y^2\right)-3\left(x+y\right)+8=2\left(x+y\right)^2-3\left(x+y\right)+8\)

\(=2.5^2-3.5+8=43\)

Vậy A=43

a) \(\left(2x+1\right)^2+2.\left(2x+1\right)+1=\left(2x+2\right)^2\)

b) \(\left(3x-2y\right)^2+4.\left(3x-2y\right)+4\)

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

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

a) \(\left(2x+1\right)^2+2\left(2x+1\right)+1=\left(2x+2\right)^2\)

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

4) \(3x^2\left(x+1\right)-2\left(x+1\right)=\left(x+1\right)\left(3x^2-2\right)\)

5) \(\left(a+b+c\right)^2-\left(ab+bc+ca\right)\left(a+b+c\right)+\left(a+b+c\right)\)

\(=\left(a+b+c\right)\left(a+b+c-ab-bc-ca+1\right)\)

6) \(4x^2\left(x-2y\right)-20x\left(2y-x\right)=4x^2\left(x-2y\right)+20x\left(x-2y\right)=4x\left(x-2y\right)\left(x+5\right)\)

7) \(3x^2y^2\left(a-b+c\right)+2xy\left(b-a-c\right)=3x^2y^2\left(a-b+c\right)-2xy\left(a-b+c\right)\\ =xy\left(a-b+c\right)\left(3xy+2\right)\)

a: \(=3\left(x^2-\dfrac{2}{3}x+\dfrac{4}{3}\right)\)

\(=3\left(x^2-2\cdot x\cdot\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{11}{9}\right)\)

\(=3\left(x-\dfrac{1}{3}\right)^2+\dfrac{11}{3}>=\dfrac{11}{3}\)

Dấu '=' xảy ra khi x=1/3

b: \(=2\left(x^2+\dfrac{3}{2}x\right)\)

\(=2\left(x^2+2\cdot x\cdot\dfrac{3}{4}+\dfrac{9}{16}-\dfrac{9}{16}\right)\)

\(=2\left(x+\dfrac{3}{4}\right)^2-\dfrac{9}{8}>=-\dfrac{9}{8}\)

Dấu '=' xảy ra khi x=-3/4

d: \(=3\left(x^2-2x+\dfrac{2}{3}\right)\)

\(=3\left(x^2-2x+1-\dfrac{1}{3}\right)\)

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

Dấu '=' xảy ra khi x=1

a) Ta có: \(\left(9x^2y^3-12x^4y^4\right):3x^2y-\left(2-3x^2y\right)\cdot y^2\)

\(=3y^2-4x^2y^3-2y^2+3x^2y^3\)

\(=y^2-x^2y^3\)

b) Ta có: \(\left[5\left(x+2y^2\right)\left(x-2y^2\right)-\left(5x-4y^2\right)\left(x+12.5y^2\right)\right]:\left(-0.3x\right)\)

\(=\left[5\left(x^2-4y^4\right)-\left(5x^2+62.5xy^2-4xy^2-50y^4\right)\right]:\left(-0.3x\right)\)

\(=\left(5x^2-20y^4-5x^2-58.5xy^2+50y^4\right):\left(-0.3x\right)\)

\(=\left(30y^4-58.5xy^2\right):\left(-0.3x\right)\)

\(=\frac{-0.3\cdot\left(-100y^4+195xy^2\right)}{-0.3x}=\frac{-100y^4+195xy^2}{x}\)

\(\left(3x-2y\right)^2\)

\(=9x^2-2.3x.2y+4y^2\)

\(=9x^2-12xy+4y^2\)

\(\left(3x+4\right)\left(5x-2\right)\)

\(=3x.5x+3x.\left(-2\right)+4.5x+4.\left(-2\right)\)

\(=10x^2+14x-8\)

Ủa, nhầm 15x²+14x-8

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