# [數學] Identity(急)

Whether each of them is Identity:

1)3x-[7x-5(3-8x)]=15-43x

2)(x-2y)^2+(x+2y)^2=2(x-2y)(x+2y)+16y^2

Identity:

1)x(x-y)+y(y-x)

2)3x^2y-12x^4y

3)16(-2x/3-y/3)(y/4-x/2)

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

5) [4(3y/2+1/6)]^2

6)(x+2y-3z)(x+2y+3z)

Rating

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