math屎(10點)

( 1 ) (a+b+1)(a+b-1) [[[[設x=a+b]]]]]

= ( x + 1 )( x - 1 )

= x^2 - 1

= ( a + b )^2 - 1

= a^2 + 2ab + b^2 - 1

( 2 ) (a+b+c+d)(a+b-c-d) [[[[[x=a+b & y=c+d]]]]

= ( x + y )( x - y )

= x^2 - y^2

= ( a + b )^2 - ( c + d )^2

= a^2 + 2ab + b^2 - c^2 - 2cd - d^2

= a^2 + b^2 - c^2 - d^2 + 2ab - 2cd

( 3 ) (ｘ^2 +ｘ+1)(ｘ^2 -ｘ+1) [[[[y=x^2+1]]]]

= ( y + x )( y - x )

= y^2 - x^2

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

= x^4 + 2x^2 + 1 - x^2

= x^4 + x^2 + 1

( 4 ) (３ｘｙ-２ｘ^2-４ｙ^2)-(-８ｘ^2-６ｘｙ+３ｙ^2)

= 3xy - 2x^2 - 4y^2 + 8x^2 + 6xy - 3y^2

= 6x^2 + 9xy - 7y^2

1(x+1)(x-1)
= x平方-1

2 (x+y)(x-y)
=x平方-y平方

3. (y+x)(y-x)
=y平方-x平方 (我當你未知數後是平方)

(３ｘｙ-２ｘ2-４ｙ2)-(-８ｘ2-６ｘｙ+３ｙ2)
=３ｘｙ-２ｘ2-４ｙ2+８ｘ2+６ｘｙ-３ｙ2
=9xy+6x平方-7y平方
(自己再對下啦)

1. (a+b+1)(a+b-1) [[[[設x=a+b]]]]]
=(x+1)(x-1)
=x^2+x-x-1
=X^2 - 1

2.
(a+b+c+d)(a+b-c-d)
=(x+y)(x-y)
=x^2+xy-xy-y^2
=x^2-y^2

3.
.(ｘ2+ｘ+1)(ｘ2-ｘ+1)
=(y+x)(y-x)
=y^2+xy-xy-x^2
=y^2-x^2

4.
(３ｘｙ-２ｘ2-４ｙ2)-(-８ｘ2-６ｘｙ+３ｙ2)
=(3xy-2x^2-4y^2)-(-8x^2-6xy+3y^2)
=3xy-2x^2-4y^2+8x^2+6xy-3y^2
=4x^2+9xy-7y^2

remark: y^2=yy, x^2=xx