Đáp án:
$a)(x^2+2y^2)(x^2+y^2)\\
b) (x^2+y^2-xy)(x^2+y^2+xy)\\
c) (x^2-4y^2)(x^2-y^2)\\
d)4(x^2-y^2)(x^2+2y^2)\\$
Giải thích các bước giải:
$a)x^4+3x^2y^2+4y^4\\
=x^4+2.x^2.(2y)^2+4y^4-x^2y^2\\
=(x^2+2y^2)^2-(xy)^2\\
=(x^2+2y^2-xy)(x^2+y^2+xy)\\
b) x^4+x^2y^2+y^4\\
=x^4+2x^2y^2+y^2-x^2y^2\\
=(x^2+y^2)^2-(xy)^2\\
=(x^2+y^2-xy)(x^2+y^2+xy)\\
c) x^4-5x^2y^2+4y^4\\
=x^4-4x^2y^2-x^2y^2+4y^4\\
=x^2(x^2-4y^2)-y^2(x^2-2y^2)\\
=(x^2-4y^2)(x^2-y^2)\\
d) 4x^4+4x^2y^2-8y^4\\
=4x^4-4y^4+4x^2y^2-4y^4\\
=4(x^4-y^4)+4y^2(x^2-y^2)\\
=4(x^2-y^2)(x^2+y^2)4y^2(x^2-y^2)\\
=4(x^2-y^2)(x^2+y^2+y^2)\\
=4(x^2-y^2)(x^2+2y^2)\\$
