分解因式.及化简求值.3

题目

分解因式.及化简求值.3
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11.(9x^4)-(13x^2×y^2)+4y^4
12.x^(n+5)-7x^(n+3)-8x^(n+1)
13.已知(a^2)+a+1=0,求(a^3)+(2a^2)+2a+3的值.
14.如果a+b=1,求(a^3)+3ab+b^3的值.
15.如果(a^2)+5a+k分解后有一个因式为(a-1),那么k的值为多少?

答案

11.9x^4-13x^2y^2+4y^4
=（x^2-y^2)（9x^2-4y^2）
=(x-y)(x+y)(3x-y)(3x+y)
12.x^(n+1)(x^4-7x^2-8)
=x^(n+1)(x^2+1)(x^2-8)
13.原式=(a^2+a+1)(a+1)+2
=2
14.原式=(a^3+b^3)+3ab
=(a+b)(a^2+b^2-ab)+3ab
=a^2+b^2+2ab
=(a+b)^2
=1
15.设(a-1)(a+m)=a^2+5a+k
则-1m=k
m-1=5
解得m=6,k=-6