Factorize－jpjzhf9的部落格

標題:

Factorize

發問:

1.(7x-2y)^2-(3x+4y)^2 2.5(a-b)^2-20(2a+3b)^2 3.27(x+2y)^2-12(x+y)^2 更新: 4.p^8-q^8

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最佳解答:

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

其他解答:

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)