Question

问点初一数学分解因式题 1：a³-a²-a+1 2:4a²+4a-4a²b+b+1 3：ax²+16ay²-a-

1：a³-a²-a+1 2:4a²+4a-4a²b+b+1 3：ax²+16ay²-a-8axy 4：ab（m²+n²）+mn（a²+b²）

速度~~~~

Answer 1

a³-a²-a+1
=a^2(a-1)-(a-1)
=(a-1)*(a^2-1)
=(a-1)*(a+1)(a-1)
=(a-1)^2(a+1)
4a²+4a-4a²b+b+1
=(4a²+4a+1)-(4a²b-b)
=(2a+1)^2-b(4a^2-1)
=(2a+1)^2-b(2a+1)(2a-1)
=(2a+1)[(2a+1)-b(2a-1)]
=(2a+1)(2a+1-2ab+b)
ax²+16ay²-a-8axy
=a(x²+16y²-1-8xy)
=a[(x-4y)^2-1]
=a(x-4y+1)(x-4y-1)
ab（m²+n²）+mn（a²+b²）
=abm²+abn²+a²mn+b²mn
=(abm²+a²mn)+(abn²+b²mn)
=am(bm+an)+bn(an+bm)
=(an+bm)(am+bn)

Answer 2

1、a³-a²-a+1=a²（a-1）-（a-1）=(a²-1)（a-1）=（a-1）²(a+1)
2、4a²+4a-4a²b+b+1=4a²+4a+1-b(4a²-1)=(2a+1)²-b(2a+1)(2a-1)=(2a+1)(2a-2ab+b+1)
3、ax²+16ay²-a-8axy=a(x²+8xy+16y²) -a=a(x+4y)²-a=a(x+4y+1)(x+4y-1)
4、ab（m²+n²）+mn（a²+b²）=a²mn+abm²+abn²+b²mn=am(an+bm)+bn(an+bm)=(am+bn)(an+bm)

Answer 3

a³-a²-a+1 2:4a²+4a-4a²b+b+1 3：ax²+16ay²-a-8axy 4：ab（m²+n²）+mn（a²+b²