Respuesta :
Square of a binomial
Initial explanation
We want to expand the following square:
[tex](8x^2-4)^2=(8x^2-4)(8x^2-4)[/tex]In order to do so, we just have to remember one simple rule:
In this case...
We have that:
[tex]\begin{gathered} (8x^2-4)(8x^2-4) \\ \downarrow \\ (8x^2)(8x^2-4)+(-4)(8x^2-4) \\ \downarrow \\ (8x^2)(8x^2)+(8x^2)(-4)+(-4)(8x^2)+(-4)(-4) \end{gathered}[/tex]Finding the result of each term:
[tex]\begin{gathered} (8x^2)(8x^2)=64x^4 \\ \mleft(8x^2\mright)\mleft(-4\mright)=-32x^2 \\ \mleft(-4\mright)\mleft(8x^2\mright)=-32x^2 \\ (-4)(-4)=16 \end{gathered}[/tex]Then,
[tex]\begin{gathered} (8x^2)(8x^2)+(8x^2)(-4)+(-4)(8x^2)+(-4)(-4) \\ =64x^4-32x^2-32x^2+16 \\ =64x^4-64x^2+16 \end{gathered}[/tex]Then, the expanded square is:
[tex]\mleft(8x^2-4\mright)^2=64x^4-64x^2+16[/tex]