Question

将下列多项式分解因式 （1）4x^3y-16xy^3 (2)2-2分之一a^2(3)(3x-y)^2-(x+3y)^2(4)a^4-16b^4

（1）4x^3y-16xy^3 (2)2-2分之一a^2(3)(3x-y)^2-(x+3y)^2(4)a^4-16b^4

Answer 1

（1）4x^3y-16xy^3
=4xy(x^2-4y^2)
=4xy(x-2y)(x+2y)

(2)2-2分之一a^2
=1/2(4-a^2)
=1/2(2-a)(2+a)

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

(4)a^4-16b^4
=(a^2+4b^2)(a^2-4b^2)
=(a^2+4b^2)(a+2b)(a-2b)

Answer 2

1）4x³y-16xy³ =4xy(x²-y²0=4xy(x+y)(x-y)
(2)2-a²/2=1/2X(4-a²)=(2+a)(2-a)/2
(3)(3x-y)²-(x+3y)²=(3x-y+x+3y)(3x-y-x-3y)=(4x+2y)(2x-4y)=4(2x+y)(x-2y)
(4)a^4-16b^4=(a²+4b²)(a²-4b²)=(a²+4b²)(a+2b)(a-2b)

Answer 3

（1）4x^3y-16xy^3 =4xy(x^2-4y^2)=4xy(x-2y)(x+2y)
(2)2-2分之一a^2=(根号2+二分之根号二 a)(根号2-二分之根号二 a)
(3)(3x-y)^2-(x+3y)^2=(3x-y-x-3y)(3x-y+x+3y)=(2x-4y)(4x+2y)
(4)a^4-16b^4=(a^2-4a^2)(a^2+4a^2)=(a+2a)(a-2a)(a^2+4a^2)