分解因式:(1)75x^2-48y^2(2)(a-b)(x-y)-(b-a)(x+y)(3)a^2+4ab+4b^2(4)3ax^3-108ax(5)81a^4-1

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分解因式:(1)75x^2-48y^2(2)(a-b)(x-y)-(b-a)(x+y)(3)a^2+4ab+4b^2(4)3ax^3-108ax(5)81a^4-1分解因式:(1)75x^2-48y^

分解因式:(1)75x^2-48y^2(2)(a-b)(x-y)-(b-a)(x+y)(3)a^2+4ab+4b^2(4)3ax^3-108ax(5)81a^4-1
分解因式:(1)75x^2-48y^2(2)(a-b)(x-y)-(b-a)(x+y)(3)a^2+4ab+4b^2(4)3ax^3-108ax(5)81a^4-1

分解因式:(1)75x^2-48y^2(2)(a-b)(x-y)-(b-a)(x+y)(3)a^2+4ab+4b^2(4)3ax^3-108ax(5)81a^4-1
分解因式:(1)75x^2-48y^2=3(25x^2-16y^2)=3(5x+4y)(5x-4y)
(2)(a-b)(x-y)-(b-a)(x+y)=(a-b)(x-y)+(a-b)(x+y)=(a-b)(x-y+x+y)=2x(a-b)
(3)a^2+4ab+4b^2=(a+2b)^2
(4)3ax^3-108ax=3ax(x^2-36)=3ax(x+6)(x-6)
(5)81a^4-1=(9a^2+1)(9a^2-1)=(9a^2+1)(3a+1)(3a-1)

1.原式=3(25x^2-16y^2)
=3[(5x-4y)(5x+4y)]
2.原式=(a-b)[(x-y)+(x+y)]
=2x(a-b)
3.原式=(a+2b)^2
4.原式=3a(x^3-36x)
=3ax(x^2-36)
=3ax(x-6)(x+6)
5.原式=(9a^2)^2-1^2
=(9a^2+1)(9a^2-1)
=(9a^2+1)(3a+1)(3a-1)

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