HSA.SSE.A.2 Tutor Intake — Rewriting Expressions Using Structure

Which of the following expressions can be factored using the
difference of squares pattern $a^2 - b^2 = (a+b)(a-b)$?

Which expression is a perfect square trinomial — one that fits
the pattern $a^2 \pm 2ab + b^2 = (a \pm b)^2$?

A student claims: "$x^2 + y^2$ can be factored as $(x + y)(x - y)$."

Which statement BEST explains why this is incorrect?

Which of the following expressions correctly identifies the
"parts" $a$ and $b$ for factoring $4x^2 - 9$ as a difference
of squares?

Factor: $x^3 - 8$.

Using the difference of cubes formula
$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$, the factored form is
$(x - 2)(x^2 + 2x + k)$ for some value $k$.

What is $k$?

A student factors $x^4 + 7x^2 + 12$ by letting $u = x^2$,
rewriting as $u^2 + 7u + 12$, and factoring it as $(u + 3)(u + 4)$.

After substituting back, the factored form of the original expression
is $(x^2 + 3)(x^2 + 4)$.

Evaluate the original expression at $x = 1$ to verify. What is the
value of $x^4 + 7x^2 + 12$ when $x = 1$?