Question

因式分解(10分)急急急急

5. a^nb^(n+1)+a^n+b
6. c^2+4ab-(a+b)^2
7. (x^2-x)^2-14(x^2-x)+24
8. (x^2+3x+1)^2+2(x^2+3x+1)-8
9. x^4-10x^2+25

Answer 1

5. a^nb^(n+1)+a^nb=a^nb(b^n+1)
6. c^2+4ab-(a+b)^2=c^2-(a-b)^2=(c+a-b)(c-a+b)
7. (x^2-x)^2-14(x^2-x)+24=(x^2-x-12)(x^2-x-2)=(x-4)(x+3)(x-2)(x+1)
8. (x^2+3x+1)^2+2(x^2+3x+1)-8=(x^2+3x+1+4)(x^2+3x+1-2)
=(x^2+3x+5)(x^2+3x-1)
9. x^4-10x^2+25 =(x^2-5)^2

Answer 2

结果如下。
a^n*b^(n+1)+a^n+b
-(-b+a-c)*(-b+a+c)
(x-2)*(x-4)*(x+3)*(x+1)
(x^2+3*x+5)*(x^2+3*x-1)
(x^2-5)^2