分解因式:x³+3ax²+﹙3a²-b²﹚x+a﹙a²-b²﹚
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![分解因式:x³+3ax²+﹙3a²-b²﹚x+a﹙a²-b²﹚](/uploads/image/z/5534467-43-7.jpg?t=%E5%88%86%E8%A7%A3%E5%9B%A0%E5%BC%8F%EF%BC%9Ax%26%23179%3B%EF%BC%8B3ax%26%23178%3B%EF%BC%8B%EF%B9%993a%26%23178%3B%EF%BC%8Db%26%23178%3B%EF%B9%9Ax%EF%BC%8Ba%EF%B9%99a%26%23178%3B%EF%BC%8Db%26%23178%3B%EF%B9%9A)
分解因式:x³+3ax²+﹙3a²-b²﹚x+a﹙a²-b²﹚
分解因式:x³+3ax²+﹙3a²-b²﹚x+a﹙a²-b²﹚
分解因式:x³+3ax²+﹙3a²-b²﹚x+a﹙a²-b²﹚
x^3+3ax^2+(3a^2-b^2)x+a(a^2-b^2)
=(x^3+3ax^2+3a^2x+a^3)-b^2x-ab^2
=(x+a)^3-b^2(x+a)
=(x+a)[(x+a)^2-b^2]
=(x+a)(x+a+b)(x+a-b)
x^3+3ax^2+(3a^2-b^2)x+a(a^2-b^2) =(x^3+3ax^2+3a^2x+a^3)-b^2x-ab^2=(x+a)^3-b^2(x+a)
=(x+a)[(x+a)^2-b^2]=(x+a)(x+a+b)(x+a-b)