Question

Expand the square of a binomial (8x^2-4)^2

Answer 1

Square of a binomial

Initial explanation

We want to expand the following square:

`(8x^2-4)^2=(8x^2-4)(8x^2-4)`

In order to do so, we just have to remember one simple rule:

In this case...

We have that:

`\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}`

Finding the result of each term:

`\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}`

Then,

`\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}`

Then, the expanded square is:

`\mleft(8x^2-4\mright)^2​=64x^4-64x^2+16`