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

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

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

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

e) \(\left(4x^2+1\right)^2-16x^2=\left(4x^2+1+4x^2\right)\left(4x^2+1-4x^2\right)=8x^2+1\)

f) \(16x^2-\left(x^2+4\right)^2=\left(4x^2+x^2+4\right)\left(4x^2-x^2-4\right)=\left(5x^2+4\right)\left(3x^2-4\right)\)

g) \(x^2+6x^2+12x+8=\left(x+2\right)^3\)

h) \(27x^3-54x^2+36x-8=\left(3x-2\right)^3\)

i) \(x^3-\dfrac{3}{2}x^2+\dfrac{3}{4}x-\dfrac{1}{8}=\left(x-\dfrac{1}{2}\right)^3\)

k) \(0,125x^3-0,75x^2+1,5x-1=\left(0,5-1\right)^3\)

thanks nha

Bài 1:

a, \(x^2+10x+26+y^2+2y\)

\(=x^2+2.x.5+5^2+y^2+2.y.1+1^2\)

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

b, \(x^2-2xy+2y^2+2y+1\)

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

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

c, \(4x^2+2z^2-4xz-2z+1\)

\(=\left(2x\right)^2-2.2x.z+z^2+z^2-2.z.1+1^2\)

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

Chúc bạn học tốt!!!

Bài1:

Bn kia giải r nhé

Bài 2:

a)\(127^2+146.127+73^2=127^2+2.73.127+73^2\)

=\(\left(127+73\right)^2=200^2=40000\)

b)\(31,8^2-63,6.21,8+21,8^2=\left(31,8-21,8\right)^2=10^2=100\)

c)\(2018^2-2017^2+2016^2-2015^2+...+2^2-1\)

=\(\left(2018+2017\right)+\left(2015+2016\right)+...+\left(2+1\right)\)

=4025+4031+...+3

=...(bn tự tính)

d)\(2017^2-2016.2018=2017^2-\left(2017^2-1\right)=1\)

1,Thực hiện phép tính :

a, (x + 2)⁹ : (x + 2)⁶

=(x+2)^9-6

=(x+2)³

b, (x - y) ⁴ : (x - 2)³

=(x-y)^4-3

=x-y

c, ( x²+ 2x + 4)⁵ : (x² + 2x + 4)

=(x²+2x+4)^5-1

=(x²+2x+4)⁴

d, 2(x² + 1)³ : 1/3(x² + 1)

=(2÷1/3).[(x²+1)³÷(x²+1)]

=6(x²+1)²

e, 5 (x - y)⁵ : 5/6 (x - y)²

=(5÷5/6).[(x-y)⁵÷(x-y)²]

=6(x-y)⁾³

bài 1

a(x+y)²-(x-y)²

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

=(x+y-x+y)(x+y+x-y)

=2y.2x

b,(3x+1)²-(x+1)²

=[(3x+1)-(x+1)][(3x+1)+(x+1)]

=(3x+1-x-1)(3x+1+x+1)

=2x.(4x+2)

4x.(x+10

bài 2

x³-0,25x=0

=>x(x²-0,25)=0

=>x=0 hoặc x²-0,25=0

=> x=0 hoặc x=\(\pm0,5\)

8) \(y^2-y-30=y^2+5y-6y-30=y\left(y+5\right)-6\left(y+5\right)=\left(y-6\right)\left(y+5\right)\)

9) \(y^2-8y+15=y^2-3y-5y+15=y\left(y-3\right)-5\left(y-3\right)=\left(y-5\right)\left(y-3\right)\)

10) \(y^2+y-6=y^2-2y+3y-6=y\left(y-2\right)+3\left(y-2\right)=\left(y+3\right)\left(y-2\right)\)

11) \(y^2-y-12=y^2+3y-4y-12=y\left(y+3\right)-4\left(y+3\right)=\left(y-4\right)\left(y+3\right)\)

12) \(x^2-5x+6=x^2-2x-3x+6=x\left(x-2\right)-3\left(x-2\right)=\left(x-3\right)\left(x-2\right)\)

13) \(u^2+u-42=u^2+7u-6u-42=u\left(u+7\right)-6\left(u+7\right)=\left(u-6\right)\left(u+7\right)\)

14) \(2x^2+x-6=2x^2+4x-3x-6=2x\left(x+2\right)-3\left(x+2\right)=\left(2x-3\right)\left(x+2\right)\)

15) \(7x^2+50x+7=7x^2+49x+x+7=7x\left(x+7\right)+\left(x+7\right)=\left(7x+1\right)\left(x+7\right)\)

16) \(12x^2+7x-12=12x^2+16x-9x-12=4x\left(3x+4\right)-3\left(3x+4\right)=\left(4x-3\right)\left(3x+4\right)\)

17) \(15x^2+7x-2=15x^2-3x+10x-2=3x\left(5x-1\right)+2\left(5x-1\right)=\left(3x+2\right)\left(5x-1\right)\)

18) \(2x^2-y^2+xy=2x^2+2xy-xy-y^2=2x\left(x+y\right)-y\left(x+y\right)=\left(2x-y\right)\left(x+y\right)\)

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

Bài 2

\( a)4{\left( {x + 1} \right)^2} + {\left( {2x - 1} \right)^2} - 8\left( {x - 1} \right)\left( {x + 1} \right) = 11\\ \Leftrightarrow 4\left( {{x^2} + 2x + 1} \right) + 4{x^2} - 4x + 1 - 8\left( {{x^2} - 1} \right) = 11\\ \Leftrightarrow 4{x^2} + 8x + 4 + 4{x^2} - 4x + 1 - 8{x^2} + 8 = 11\\ \Leftrightarrow 4x + 13 = 11\\ \Leftrightarrow 4x = 11 - 13\\ \Leftrightarrow 4x = - 2\\ \Leftrightarrow x = - \dfrac{1}{2} \)

Bài 2:

\( b)\left( {x - 3} \right)\left( {{x^2} + 3x + 9} \right) + x\left( {x + 2} \right)\left( {2 - x} \right) = 1\\ \Leftrightarrow {x^3} - 27 + x\left( {2 + x} \right)\left( {2 - x} \right) = 1\\ \Leftrightarrow {x^3} - 27 + x\left( {4 - {x^2}} \right) = 1\\ \Leftrightarrow {x^3} - 27 + 4x - {x^3} = 1\\ \Leftrightarrow 4x = 1 + 27\\ \Leftrightarrow 4x = 28\\ \Leftrightarrow x = 7 \)

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

2)\(9x^2-24xy+16y^2=\left(3x-4y\right)^2\)

3)\(-x^2+10x-25=-\left(x-5\right)^2\)

4)\(1+12x+36x^2=\left(1+6x\right)^2\)

5) \(\dfrac{x^2}{4}+2xy+4y^2=\left(\dfrac{x}{2}+2y\right)^2\)

6) \(4x^2+4xy+y^2=\left(2x+y\right)^2\)

bài toán iêu cầu j z ??? bn