Question

因式分解好几道不会

x^2-10xy+9y^2=_________
2010^2-2009^2=__________
x^2+5x-6=(x+__)^2+____
3x^2+10x-8=_________
9-a^2-b^2-2ab=________
ax^2+ay^2-2axy-a^3=________
a^4+a^2b^2+b^4=________

(学过因式分解的解答下下、需过程、拜托了、感激不尽)

Answer 1

x^2-10xy+9y^2=（x-y)(x-9y)

2010^2-2009^2=(2010+2009)(2010-2009)=4019*1=4019

x^2+5x-6=(x+2.5)^2-(3.5)^2
=(x+2.5+3.5)(x+2.5-3.5)
=(x+6)(x-1）

3x^2+10x-8
=(x+4)(3x-2)

9-a^2-b^2-2ab
=3^2-(a+b)^2
=(3+a+b)(3-a-b)

ax^2+ay^2-2axy-a^3
=a[(x^2+y^2-2xy)-a^2]
=a[(x-y)^2-a^2]
=a(x-y+a)(x-y-a)

a^4+a^2b^2+b^4
=a^4+2a^2b^2+b^4-a^2b^2
=(a^2+b^2)^2-(ab)^2
=(a^2+b^2+ab)(a^2+b^2-ab)