Answer:
[tex]\left(ab^2x-b^4a^3\right)^2:\quad a^2b^4x^2-2a^4b^6x+a^6b^8[/tex]
Step-by-step explanation:
Given the expression
[tex]\left(ab^2\:x\:-b^4a^3\right)^2[/tex]
solving the expression
[tex]\left(ab^2\:x\:-b^4a^3\right)^2[/tex]
[tex]\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a-b\right)^2=a^2-2ab+b^2[/tex]
[tex]a=ab^2x,\:\:b=b^4a^3[/tex]
so the expression becomes
[tex]=\left(ab^2x\right)^2-2ab^2xb^4a^3+\left(b^4a^3\right)^2[/tex]
[tex]=a^2b^4x^2-2a^4b^6x+a^6b^8[/tex]
Thus,
[tex]\left(ab^2x-b^4a^3\right)^2:\quad a^2b^4x^2-2a^4b^6x+a^6b^8[/tex]
