Factorize

1.(7x-2y)^2-(3x+4y)^2

=(7x-2y+3x+4y)(7x-2y-3x-4y)

=(10x+2y)(4x-6y)

=4(5x+y)(2x-3y)

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2.5(a-b)^2-20(2a+3b)^2

=5[(a-b)^2-4(2a+3b)^2]

=5{(a-b)^2-[2(2a+3b)^2]}

=5[(a-b-4a-6b)(a-b+4a+6b)]

=5(-3a-7b)(5a+5b)

=25(-3a-7b)(a+b)

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3.27(x+2y)^2-12(x+y)^2

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

=3[3x+6y+2x+2y][3x+6y-2x-2y]

=3(5x+8y)(x+4y)

2007-03-31 13:43:04 補充：
--------------------------------------------------------------------4.p^8-q^8=(p^4+q^4)(p^4-q^4)=(p^4+q^4)(p^2-q^2)(p^2+q^2)=(p^4+q^4)(p^2+q^2)(p+q)(p-q)

1. (7x-2y)^2-(3x+4y)^2
= ((7x-2y) + (3x+4y)) ((7x-2y) - (3x+4y))
---> a^2 - b^2 = (a+b)(a-b)
= (7x-2y+3x+4y) (7x-2y-3x-4y)
= (10x-2y)(4x-6y)
= (2)(5x-y) (2)(2x-3y)
= 4(5x-y)(2x-3y)

2. 5(a-b)^2-20(2a+3b)^2
= 5(a^2 - 2ab + b^2) - 20(4a^2 +12ab +9b^2)
= 5 [(a^2 - 2ab + b^2) - 4(4a^2 +12ab +9b^2)]
= 5 (a^2 - 2ab + b^2 - 16a^2 - 48ab - 36b^2)
= 5 (-15a^2 -50ab - 35b^2)
= 5 (-5) (3a^2 + 10ab + 7b^2)
= -25 (3a+7b) (a+b)

3. 27(x+2y)^2-12(x+y)^2
= 15x^2 + 84xy+ 96y^2
= 3(8y+5x)(4y+x)