A=\(\left(x-y\right)^2+\left(x+y\right)^2=x^2-2xy+y^2+x^2+2xy+y^2=2x^2+2y^2\)
B=\(\left(x+y\right)^2-\left(x-y\right)^2=\left(x+y-x+y\right)\left(x+y+x-y\right)=\left(2y\right).\left(2x\right)\)
C=\(\left(2a+b\right)^2-\left(2a-b\right)^2=\left(2a+b-2a+b\right)\left(2a+b+2a-b\right)=\left(2b\right).\left(4a\right)\)
D=\(\left(2x-1\right)^2-2\left(2x-3\right)^2+4=4x^2-4x+1-4x+6+4=4x^2-8x+11\)
E=\(\left(x+3y\right)^2-\left(x-3y\right)^2=\left(x+3y-x+3y\right)\left(x+3y+x-3y\right)=\left(6y\right).\left(2x\right)\)
F=\(\left(2x+y\right)^2-\left(2x-y\right)^2=\left(2x+y-2x+y\right)\left(2x+y+2x-y\right)=\left(2y\right).\left(4x\right)\)
G=\(\left(x-2y\right)^2+4\left(x-2y\right)y+4y^2=x^2-4xy+4y^2+4xy-8y^2+4y^2=x^2\)
H=\(\left(x-y\right)^2-4\left(x-y\right)\left(x+2y\right)+4\left(x+2y^{ }\right)^2=x^2-2xy+y^2-4\left(x^2+2xy-xy-2y^2\right)+4x+8y=x^2-2xy+y^2-4x^2-8xy+4xy+8y^2+4x+8y=3x^2+12xy-9y^2+4x+8y\)
Ta có:
a) A= (x-y)^2 + (x+y)^2
A= x^2 -2xy + y^2 + x^2 + 2xy + y^2
A= 2x^2+ 2y^2
b) B= (x+y)^2 -( x-y)^2
B= (x+y-x+y)(x+y+x-y)
B= 2y.2x= 4xy
c) C= (2a+b)^2 -( 2a-b)^2
C= (2a+b-2a+b)(2a+b+2a-b)
C= 2b.4a
C= 8ab
d) D= (2x-1)^2 -2(2x-3)^2+4
D= 4x^2 -4x+1 -2( 4x^2 -12x + 9) +4
D= 4x^2 -4x+1 -8x^2 + 24x -18 +4
D= -4x^2 + 20x-13
e) E= (x+3y)^2-(x-3y)^2
E= (x+3y-x+3y)(x+3y+x-3y)
E= 6y.2x= 12xy
f) F= (2x+y)^2-(2x-y)^2
F=(2x+y-2x+y)(2x+y+2x-y)
F= 2y.4x= 8xy
g) G= (x-2y)^2 + 4(x-2y)y + 4y^2
G= (x-2y)^2 + 2(x-2y)2y + (2y)^2
G= (x-2y+2y)^2
G= x^2
h) H= (x-y)^2 -4(x-y)(x+2y)+ 4(x+2y)^2
H= (x-y)^2 - 2(x-y)2(x+2y) + [2(x+2y)]^2
H= (x-y- 2x-4y)^2
H= (-x-5y)^2
Lưu ý (-A-B)^2 = ( A+ B)^2
=> H= (x+5y)^2
