Question

因式分解 急急急!!!!!!!!!(10分)

1. x^2-4ax+8ab-4b^2
2. (a+b)(a-b)-ab-b^2
3. (ax+by)^2+(ay-6x)^2
4. x^2-xy-1+4分之1y^2
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

1.x²-4ax+8ab-4b²
=x²-4b²-4ax+8ab
=(x-2b)(x+2b)-4a(x-2b)
=(x-b)(x+2b-4a)
2.(a+b)(a-b)-ab-b²
=a²-b²-ab-b²
=a²-ab-2b²
=(a-2b)(a+b)
3.(ax+by)²+(ay-bx)²(怀疑你题抄错了，后面的括号里是bx吧，不是6x)
=a²x²+b²y²+2abxy+a²y²+b²x²旦肆渣-2abxy
=a²x²+b²y²+a²y²+b²x²
=a²(x²+y²)+b²(x²+y²)
=(x²+y²)(a²+b²模悄)
4.x²-xy-1+y²/4
=(x-y/2)²-1
=(x- y/2 -1)(x- y/2 +1)
6. c²+4ab-(a+b)²
=c²+4ab-a²-b²-2ab
=c²-(a-b)²
=(c+a-b)(c-a+b)

7. (x²-x)²-14(x²-x)+24
=(x²-x-2)(x²雹棚-x-12)
=(x+1)(x-2)(x+3)(x-4)

8. (x²+3x+1)²+2(x²+3x+1)-8
=(x²+3x+1+4)(x²+3x+1-2)
=(x²+3x+5)(x²+3x-1)

9. x^4-10x²+25
=(x²-5)²
=(x-5)²(x+5)² .