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Proving Polynomial Identities

Proving Polynomial Identities 1.4 - 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, with $a = x$ and $b = 9.$
$(x + 9)(x - 9)$
$x^2 - 9^2$
$x^2 - 81$
b
We proceed in the same way as in the previous part to rewrite the expression using the difference of squares.
$(4 + y)(4 - y)$
$4^2 - y^2$
$16 - y^2$
c
Here, the terms are not placed in the same order inside the parentheses. However, if we change the order of the terms in $(a+7)$, they do!
$(7 - a)(a + 7)$
$(7 - a)(7 + a)$
$7^2 - a^2$
$49 - a^2$