數學 questions

1) 用恆等式: a^2 - b^2 = ( a + b )( a - b ),

( 3 - m )^2 - 144

= ( 3 - m)^2 - 12^2

= [ ( 3 - m ) + 12 ][ ( 3 - m - 12 )]

= ( 3 - m + 12 )( 3 - m -12 )

= ( 15 - m )( - 9 - m )

= ( m - 15 )( m + 9 )

2) 用十字相乘法:

2a + 1

3a - 2

---------------

3a - 4a = -a

所以6a^2 - a - 2 = ( 2a + 1 )( 3a - 2 )

3) 用十字相乘法:

2a + 5b

3a - b

----------------------

15ab - 2ab = 13ab

所以6a^2+13ab-5b^2 = ( 2a + 5b )( 3a - b )

4) 用十字相乘法:

-2a- 6b

2a - b

---------------------------

-12ab + 2ab = -10ab

所以-4a^2-10ab+6b^2

= ( - 2a - 6b )( 2a - b )

= -2 ( a + 3b )( 2a - b )

5) 192a^3-375b^3

= 3 ( 64a^3 - 125b^3 )

= 3 [ ( 4a )^3 - ( 5b )^3 ]

= 3 ( 4a - 5b )( 16a^2 + 20ab + 25b^2 )

[用恆等式:a^3 - b^3=(a-b)(a^2+ab+b^2)]




2007-10-03 23:14:10 補充：
8x^3-125y^3 = (2x)^3 - (5y)^3= ( 2x - 5y )( 4x^2 + 10y + 25y^2 )[用恆等式:a^3 - b^3=(a-b)(a^2+ab+b^2)]

1)(3-m)^2-144
=9-2m+(m^2)-144
=(m^2)-6m-135
=(m+9)(m-15)

2)6a^2-a-2
=(2a+1)(3a-1)

3)6a^2+13ab-5b^2
=(2a+5b)(3a-b)

4)-4a^2-10ab+6b^2
=(a+3b)(-4a+2b)

5)192a^3-375b^3
={[192^(1/3)]a-[375^(1/3)]b}{[192^(2/3)](a^2)+{[192^(1/3)][375^(1/3)]ab-[375^(2/3)]b}
={[192^(1/3)]a-[375^(1/3)]b}{[192^(2/3)](a^2)+{[72000^(1/3)]ab-[375^(2/3)]b}

1
(3-m+12)(3-m-12)
=(15-m)(-m-9)
=-(15-m)(m+9)
2
(3a-2)(2a+1)
3
(3a-b)(2a+5b)
4
-2(2a-b)(a+3b)
5
3(4a-5b)(16a^2+20ab+25b^2)