Question

1.Thu gọn

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

b)\(\left(x^2+x+2\right)^2+\left(x-1\right)^2-2\left(x^2+x+2\right)\left(x-1\right)\)

c)\(8x^3-12x^2y^2+6xy^4-y^6\)

d)\(-125x^3+225x^2-135x+27\)

2.CMR

a)\(x^2-6x+10>0\)

b)\(x^2-4xy+4y^2+1>0\)

c)\(x^2-4x+7\ge3\)

d)\(x^2+y^2-2x+4y+5\ge0\)

Bác nào tốt bụng làm hết giùm em với :((

Answer 1

Bài 2:

a, \(x^2-6x+10=x^2-6x+9+1\)

\(=\left(x-3\right)^2+1\ge1>0\)

\(\Rightarrowđpcm\)

b, \(x^2-4xy+4y^2+1=\left(x-2y\right)^2+1>0\)

\(\Rightarrowđpcm\)

c, \(x^2-4x+7=x^2-4x+4+3\)

\(=\left(x-2\right)^2+3\ge3\)

\(\Rightarrowđpcm\)

d, \(x^2+y^2-2x+4y+5\)

\(=x^2-2x+1+y^2+4y+4\)

\(=\left(x-1\right)^2+\left(y+2\right)^2\ge0\)

\(\Rightarrowđpcm\)

Answer 2

Ép người quá đáng >.<

Bài 1:

a, \(-\left(2x^2+2x+1\right)\left(2x^2-2x+1\right)+\left(2x^2+1\right)\)

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

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

b, \(\left(x^2+x+2\right)^2+\left(x-1\right)^2-2\left(x^2+x+2\right)\left(x-1\right)\)

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

d, \(-125x^3+225x^2-135x+27\)

\(=-\left(125x^3-225x^2+135x-27\right)\)

\(=-\left(125x^3-75x^2-150x^2+90x+45x-27\right)\)

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

\(=-\left[\left(5x-3\right)\left(25x^2-15x-15x+9\right)\right]\)

\(=-\left(5x-3\right)^3\)

Answer 3

c)\(8x^3-12x^2y^2+6xy^4-y^6=\left(2x\right)^3-12x^2y^2+6xy^4-\left(y^2\right)^3\)

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

d)\(-125x^3+225x^2-135x+27=-125x^3+75x^2+150x^2-90x-45x+27=-25x^2.\left(5x-3\right)+30x\left(5x-3\right)-9.\left(5x-3\right)=\left(5x-3\right)\left(-25x^2+30x-9\right)=-\left(5x-3\right)\left(5x-3\right)^2=-\left(5x-3\right)^3\)2 câu kia ngại lắm

Answer 4

Akai Haruma

Answer 5

Ai làm bài 1 cho mình cái

Answer 6

lm rồi mak bác =="

Answer 7

Dùng công thức nhân đa thức vs đa thức ở 2 câu a, b bài 1