[數學] Identity(急)

我有幾條identity既數想問問大家,希望大家幫下幫我,唔該!THX~

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)

請大家列清楚D步驟同答案,唔該晒大家

1 Answer

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  • 1 decade ago
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    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

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