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# Proving Polynomial Identities

## Proving Polynomial Identities 1.6 - Solution

a
The difference of squares has the form $(a - b)(a + b) = a^2 - b^2$ and we see that our expression has the same form, where $a=p$ and $b = 64$.
$\left(p-64\right)\left(p+64\right)$
$p^2 - 64^2$
$p^2 - 4096$
b
The difference of squares has the form $(a + b)(a - b) = a^2 - b^2$ and we see that our expression has the same form, with $a=x$ and $b = 2y$.
$(x+2y)(x-2y)$
$x^2 - (2y)^2$
$x^2 - 2^2y^2$
$x^2 - 4y^2$
c
We proceed in the same way to rewrite the expression with the difference of two squares. Note that the square of $x^2$ is $(x^2)^2.$
$\left(x^2-8\right)\left(x^2+8\right)$
$\left(x^2\right)^2 - 8^2$
$x^4 - 8^2$
$x^4 - 64$