f3 mth questions!!!急~聽日要交!

I help you answering the questions of different types.

You can use the skills to answer those left.


1. x^4 + x^2y^2 + y^4 Ans = ( x^2 + y^2 )^2 - x^2y^2
= ( x^2 + xy + y^2 )( x^2 - xy + y^2 )
2. 2bd – a^2 – c^2 + b^2 + d^2 + 2ac

Ans = ( b^2 - 2bd + d^2 ) - ( a^c - 2ac + c^2 )
= ( b - d )^2 - ( a - c )^2
= [ ( b - d ) + ( a - c ) ][ ( b - d ) - ( a - c ) ]
= (a + b - c - d )( -a + b + c - d )


3. 12x^2 – 8x

Ans = 4x( 3x - 2 )


4. 15a^2 bc – 21ab^2 c + 9abc^2

Ans = 3abc ( 5a - 7b + 3c )


5. 3a ^2 – 3b^2 + a^2 + 2ab + b^2

Ans = 3( a + b )( a - b ) + ( a + b )^2
= ( a + b )[ 3( a - b )+ ( a + b ) ]
= ( a + b )( 4a -2b )
= 2( a + b )( 2a - b )


6. 30x^2 + 37ax – 84a ^2

Ans = ( 6x - 7a )( 5x + 12a )


7. a^5 – 5a ^4b + 10a ^3b^3 – 10a ^2b^3

Ans = a^2 ( a^3 - 5a^2 b + 10ab^3 - 10b^3 )


8. (6x – 7y)^2 – (3x + 3y)^2

Ans = [ ( 6x - 7y ) + ( 3x + 3y ) ][ ( 6x - 7y ) - ( 3x + 3y ) ]
= ( 9x - 4y )( 3x - 10y )


9. 5(x + 2)^2 + 4(x + 2) – 12

Ans = [ 5( x + 2 ) - 6 ][ ( x + 2 ) + 2 ]
= ( 5x + 4 )( x + 4 )


10. 3(x + y)^2 – 4x - 4y +1

Ans = 3( x + y )^2 - 4( x + y ) + 1
= [ 3( x + y ) - 1 ][ ( x + y ) - 1 ]
= ( 3x + 3y - 1 )( x - y - 1 )

Hope I can help you.

Cheers!!

x^4 + x^2y^2 + y^4
(x^4+2x^2y^2+y^4)-x^2y^2
(x^2+y^2)^2-x^2y^2
(x^2-xy+y^2)(x^2+xy+y^2)

題 81 可能把錯了。