Đáp án:
$e)
(5b^2-x-2)(5b^2+x+2)\\
f)
(a-x-b-y)(a-x+b+y)\\
g) a(a-b)^2\\
8)
2(x-1-y)(x-1+y)\\
9)
(a-1)(a^2-1)\\
10)
(y-1)(3x+y+1)\\
11)
(m+y)(m-y+a)\\
12)
(x^2-y^2)(x+y)$
Giải thích các bước giải:
$e)
25b^4-x^2-4x-4\\
=(5b^2)^2-(x^2+4x+4)\\
=(5b^2)^2-(x+2)^2=(5b^2-x-2)(5b^2+x+2)\\
f)
a^2-2ax-b^2-2by+x^2-y^2\\
=(a^2-2ax+x^2)-(b^2+2by+y^2)\\
=(a-x)^2-(b+y)^2\\
=(a-x-b-y)(a-x+b+y)\\
g) a^3-2a^2b+ab^2\\
=a(a^2-2ab+b^2)\\
=a(a-b)^2\\
8)
2x^2-4x+2-2y^2\\
=2(x^2-2x+1-y^2)\\
=2.\left [ (x^2-2x+1)-y^2 \right ]\\
=2.\left [ (x-1)^2-y^2 \right ]\\
=2(x-1-y)(x-1+y)\\
9)
a^3-a^2-a+1\\
=a^2(a-1)-(a-1)\\
=(a-1)(a^2-1)\\
10)
3xy+y^2-3x-1\\
=(3xy-3x)+(y^2-1)\\
=3x(y-1)+(y-1)(y+1)\\
=(y-1)(3x+y+1)\\
11)
m^2+am+ay-y^2\\
=(m^2-y^2)+(am+ay)\\
=(m-y)(m+y)+a(m+y)\\
=(m+y)(m-y+a)\\
12)
x^3-xy^2+x^2y-y^3\\
=x(x^2-y^2)+y(x^2-y^2)\\
=(x^2-y^2)(x+y)$
