Đáp án:
$a) 4a^3b^3(2b-3a+1)\\
b)(2a+3)(x-y-1)\\
c)x(a+b-c)(x+1)\\
d) (9a+1)^2\\
e)(a-b+c)^2\\
f) (3a-x-y)(3a+x+y)\\
g)x(x+y)(x-z)\\
h)(ax+by)(a-2b)\\
i) (b-c)(a^2+bc-ab-ac)\\
k) (x-y)(z-x+y)\\$
Giải thích các bước giải:
$a) 8a^3b^4-12a^4b^3+4a^3b^3\\
=4a^3b^3(2b-3a+1)\\
b) (2a+3)x-(2a+3)y-2a-3\\
=(2a+3)x-(2a+3)y-(2a+3)\\
=(2a+3)(x-y-1)\\
c) (a+b-c)x^2-(c-a-b)x\\
=(a+b-c)x^2+(a+b-c)x\\
=x(a+b-c)(x+1)\\
d) 81a^2+18a+1\\
=(9a)^2+2.9a.1+1\\
=(9a+1)^2\\
e) (a-b)^2-2(b-a)c+c^2\\
=(a-b)^2+2.(a-b).c+c^2\\
=(a-b+c)^2\\
f) 9a^2-x^2-2xy-y^2\\
=(3a)^2-(x^2+2xy+y^2)\\
=(3a)^2-(x+y)^2\\
=(3a-x-y)(3a+x+y)\\
g) x^3+x^2y-x^2z-xyz\\
=x^2(x+y)-xz(x+y)\\
=x(x+y)(x-z)\\
h) a^2x+aby-2abx-2b^2y\\
=a(ax+by)-2b(ax+by)\\
=(ax+by)(a-2b)\\
i) a^2(b-c)+b^2(c-a)+c^2(a-b)\\
=a^2b-a^2c+b^2c-ab^2+ac^2-bc^2\\
=b(a^2+bc)-c(a^2+bc)-a(b^2-c^2)\\
=(a^2+bc)(b-c)-a(b-c)(b+c)\\
=(b-c)(a^2+bc-ab-ac)\\
k) xz-yz-x^2+2xy-y^2\\
=z(x-y)-(x^2-2xy+y^2)\\
=z(x-y)-(x-y)^2\\
=(x-y)(z-x+y)\\$
