题目真多!还是把做完了,累倒不累,就是眼花得厉害!
①立方差公式：a^3-b^3=(a-b)(a^2+ab+b^2)此题a=2m,b=1
(8m^3)-1=(2m-1)(4m^2+2m+1)
②立方和公式：a^3+b^3=(a+b)(a^2-ab+b^2)此题a=x^n,b=1
（x^3n)+1=(x^n+1)(x^2n-x^n+1)
③提公因式a^3m
(a^3m)-a^(3m+3)=a^3m(1-a)(1+a+a^2)
④(a+b)^3-(a-b)^3
[(a+b)-(a-b)][(a+b)^2+(a+b)(a-b)+(a-b)^2]
=2b[a^2+2ab+b^2+a^2-b^2+a^2-2ab+b^2]
=2b(3a^2+b^2)
=6a^2b+2b^3
⑤提公因式(x+y)(x-y)
(x+y)^4(x-y)-(y+x)(y-x)^4
=(x+y)(x-y)[(x+y)^3+(x-y)^3]
=(x+y)(x-y){[(x+y)+(x-y)][(x+y)^2-(x+y)(x-y)+(x-y)^2]}
=2x(x+y)(x-y)(x^2-3y^2)
⑥(x+1)(x^2-x+1)-1-y^3
=x^3+1-1-y^3
=x^3-y^3
=(x-y)(x^2+xy+y^2)
⑦(-27a^3)+64b^3
=(4b)^3-(3a)^3
=(4b-3a)(16b^2+12ab+9a^2)
⑧题错,改为：
(x^4)-(4x^2)+8x-16
=x^4-4x^2+8x-16
=x^2(x^2-4)+8(x-2)
=x^2(x+2)(x-2)+8(x-2)
=(x-2)[x^2(x+2)+8]
=(x-2)(x^3+2x^2+8)
⑨(x^4)-(4x^2)+3
=(x^2-1)(x^2-3)
=(x+1)(x-1)(x+√3)(x-√3)
⑩(a^8)+(a^4)-2
=(a^4-1)(a^4+2)
=(a^2-1)(a^2+1)(a^4+2)
=(a+1)(a-1)(a^2+1)(a^4+2)
11.(9x^4)-(13x^2×y^2)+4y^4
=（x^2-y^2)（9x^2-4y^2）
=(x-y)(x+y)(3x-y)(3x+y)
12.x^(n+5)-7x^(n+3)-8x^(n+1)
=x^(n+1)(x^4-7x^2-8)
=x^(n+1)(x^2+1)(x^2-8)
=x^(n+1)(x^2+1)(x+2√2)(x-2√2)
13.已知(a^2)+a+1=0,求(a^3)+(2a^2)+2a+3的值.
原式=(a^2+a+1)(a+1)+2
=2
14.如果a+b=1,求(a^3)+3ab+b^3的值.
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.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?
设(a-1)(a+m)=a^2+5a+k则
-1m=k
m-1=5
解得m=6,k=-6