Question

(ab^2 x -b^4a^3)^2

What is the answers

Answer 1

`\left(ab^2x-b^4a^3\right)^2:\quad a^2b^4x^2-2a^4b^6x+a^6b^8`

Explanation:

Given the expression

`\left(ab^2\:x\:-b^4a^3\right)^2`

solving the expression

`\left(ab^2\:x\:-b^4a^3\right)^2`

`\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a-b\right)^2=a^2-2ab+b^2`

`a=ab^2x,\:\:b=b^4a^3`

so the expression becomes

`=\left(ab^2x\right)^2-2ab^2xb^4a^3+\left(b^4a^3\right)^2`

`=a^2b^4x^2-2a^4b^6x+a^6b^8`

Thus,

`\left(ab^2x-b^4a^3\right)^2:\quad a^2b^4x^2-2a^4b^6x+a^6b^8`