1: Đây là các biểu thức thuộc hằng đằng thức bình phương của tổng

a: \(\left(2x+1\right)^2=\left(2x\right)^2+2\cdot2x\cdot1+1^2=4x^2+4x+1\)

b: \(\left(x+2y\right)^2=x^2+2\cdot x\cdot2y+\left(2y\right)^2=x^2+4xy+4y^2\)

c: \(\left(3x+2y\right)^2=\left(3x\right)^2+2\cdot3x\cdot2y+\left(2y\right)^2=9x^2+12xy+4y^2\)

d: \(\left(2+3m\right)^2=2^2+2\cdot2\cdot3m+\left(3m\right)^2=4+12m+9m^2\)

e: \(\left(3m+4n\right)^2=\left(3m\right)^2+2\cdot3m\cdot4n+\left(4n\right)^2=9m^2+24mn+16n^2\)

f: \(\left(\frac12x+\frac13y\right)^2=\left(\frac12x\right)^2+2\cdot\frac12x\cdot\frac13y+\left(\frac13y\right)^2=\frac14x^2+\frac13xy+\frac19y^2\)

g: \(\left(\frac23x+\frac32y\right)^2=\left(\frac23x\right)^2+2\cdot\frac23x\cdot\frac32y+\left(\frac32y\right)^2=\frac49x^2+2xy+\frac94y^2\)

h: \(\left(\frac32m+\frac12n\right)^2=\left(\frac32m\right)^2+2\cdot\frac32m\cdot\frac12n+\left(\frac12n\right)^2=\frac94m^2+\frac32mn+\frac14n^2\)

i: \(\left(\frac15y+\frac14z\right)^2=\left(\frac15y\right)^2+2\cdot\frac15y\cdot\frac14z+\left(\frac14z\right)^2=\frac{1}{25}y^2+\frac{1}{10}yz+\frac{1}{16}z^2\)

k: \(\left(\frac45x+\frac12y\right)^2=\left(\frac45x\right)^2+2\cdot\frac45x\cdot\frac12y+\left(\frac12y\right)^2=\frac{16}{25}x^2+\frac45xy+\frac14y^2\)

2: Đây là các biểu thức thuộc hằng đằng thức bình phương của hiệu

a: \(\left(2x-1\right)^2=\left(2x\right)^2-2\cdot2x\cdot1+1^2=4x^2-4x+1\)

b: \(\left(x-2y\right)^2=x^2-2\cdot x\cdot2y+\left(2y\right)^2=x^2-4xy+4y^2\)

c: \(\left(3x-2y\right)^2=\left(3x\right)^2-2\cdot3x\cdot2y+\left(2y\right)^2=9x^2-12xy+4y^2\)

d: \(\left(2-3m\right)^2=2^2-2\cdot2\cdot3m+\left(3m\right)^2=4-12m+9m^2\)

e: \(\left(3m-4n\right)^2=\left(3m\right)^2-2\cdot3m\cdot4n+\left(4n\right)^2=9m^2-24mn+16n^2\)

f: \(\left(\frac12x-\frac13y\right)^2=\left(\frac12x\right)^2-2\cdot\frac12x\cdot\frac13y+\left(\frac13y\right)^2=\frac14x^2-\frac13xy+\frac19y^2\)

g: \(\left(\frac23x-\frac32y\right)^2=\left(\frac23x\right)^2-2\cdot\frac23x\cdot\frac32y+\left(\frac32y\right)^2=\frac49x^2-2xy+\frac94y^2\)

h: \(\left(\frac32m-\frac12n\right)^2=\left(\frac32m\right)^2-2\cdot\frac32m\cdot\frac12n+\left(\frac12n\right)^2=\frac94m^2-\frac32mn+\frac14n^2\)

i: \(\left(\frac15y-\frac14z\right)^2=\left(\frac15y\right)^2-2\cdot\frac15y\cdot\frac14z+\left(\frac14z\right)^2=\frac{1}{25}y^2-\frac{1}{10}yz+\frac{1}{16}z^2\)

k: \(\left(\frac45x-\frac12y\right)^2=\left(\frac45x\right)^2-2\cdot\frac45x\cdot\frac12y+\left(\frac12y\right)^2=\frac{16}{25}x^2-\frac45xy+\frac14y^2\)

3: Các biểu thức này thuộc hằng đẳng thức hiệu hai bình phương

a: \(m^2-n^2=\left(m-n\right)\left(m+n\right)\)

b: \(4m^2-16n^2=\left(2m\right)^2-\left(4n\right)^2=\left(2m-4n\right)\left(2m+4n\right)\)

c: \(49-16x^2=\left(7-4x\right)\left(7+4x\right)\)

d: \(25-9y^2=5^2-\left(3y\right)^2=\left(5-3y\right)\left(5+3y\right)\)

e: \(81x^2-16y^2=\left(9x\right)^2-\left(4y\right)^2=\left(9x-4y\right)\left(9x+4y\right)\)

f: \(\frac{1}{16}x^2-\frac{1}{25}y^2=\left(\frac14x-\frac15y\right)\left(\frac14x+\frac15y\right)\)

g: \(\frac{1}{81}x^2-\frac{4}{25}y^2=\left(\frac19x-\frac25y\right)\left(\frac19x+\frac25y\right)\)

h: \(\frac{49}{16}m^2-\frac{16}{25}n^2=\left(\frac74m\right)^2-\left(\frac45n\right)^2=\left(\frac74m-\frac45n\right)\left(\frac74m+\frac45n\right)\)

i: \(\frac{81}{16}x^2-\frac{16}{49}y^2=\left(\frac94x\right)^2-\left(\frac47y\right)^2=\left(\frac94x-\frac47y\right)\left(\frac94x+\frac47y\right)\)

k: \(\frac{16}{81}x^2-\frac{1}{36}y^2=\left(\frac49x-\frac16y\right)\left(\frac49x+\frac16y\right)\)