Answer:
The simplified form of the given product [tex]\left(4x\:-\:6y^3\right)^2\:[/tex] is [tex]16x^2-48xy^3+36y^6[/tex]
Step-by-step explanation:
Given: Expression [tex]\left(4x\:-\:6y^3\right)^2\:[/tex]
We have to write the simpler form of the given product [tex]\left(4x\:-\:6y^3\right)^2\:[/tex]
Consider the given expression [tex]\left(4x\:-\:6y^3\right)^2\:[/tex]
Apply perfect square identity [tex]\left(a-b\right)^2=a^2-2ab+b^2[/tex]
[tex]a=4x,\:\:b=6y^3[/tex]
We have,
[tex]=\left(4x\right)^2-2\cdot \:4x\cdot \:6y^3+\left(6y^3\right)^2[/tex]
Simplify, we have,
[tex]=16x^2-48xy^3+36y^6[/tex]
Thus, The simplified form of the given product [tex]\left(4x\:-\:6y^3\right)^2\:[/tex] is [tex]16x^2-48xy^3+36y^6[/tex]
