1:a³-a²-a+1 2:4a²+4a-4a²b+b+1 3:ax²
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/10/06 08:54:00
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)
1:a³-a²-a+1 2:4a²+4a-4a²b+b+1 3:ax²+16ay²-a-8axy 4:ab(m²+n²)+mn(a²+b²)
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)
=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)
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