[數學] Identity(急)

Whether each of them is Identity:
1)3x-[7x-5(3-8x)]=15-43x
3x-[7x-15+40x]=15-43x
3x-[47x-15]=15-43x
3x-47x+15=15-43x
-44x+15=15-43x
This is not identity since left side is not equal to right side

2) (x-2y)^2+(x+2y)^2 = 2(x-2y)(x+2y)+16y^2
x^2 -4xy +y^2 + x^2 +4xy +y^2 = 2(x^2 – 4y^2) +16y^2
x^2 +y^2 + x^2 +y^2 = 2(x^2 – 4y^2) +16y^2
2x^2 +2y^2 = 2x^2 – 8y^2 +16y^2
2x^2 +2y^2 = 2x^2 + 8y^2
This is not identity since left side is not equal to right side

Identity: (What do you mean? Either expand or factorize?)

1)x(x-y)+y(y-x)
= x(x – y) – y(x – y)
= (x-y) (x – y) = (x-y)^2

2)3x^2y-12x^4y = 3x^2y(1 – 4x^2)
= 3x^2y(1 + 2x)(1 – 2x)

3)16(-2x/3-y/3)(y/4-x/2)
= 16(-2/3x – 1/3 y)(-1/2x +1/4 y)
= 16(1/3x^2 – 1/12y^2)

4)[(a+b)(a-b)]^2
= (a^2 – b^2)^2
= (a^4 – 2a^2b^2 +b^4)

5) [4(3y/2+1/6)]^2
=16(3y/2+1/6)^2
= 36y^2 +8y +4/9

6)(x+2y-3z)(x+2y+3z)
= (x+2y)^2 – (3z)^2