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

题目

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

答案

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=(9...