Question

drag the tiles to the boxes to form correct pairs. not all tiles will be used.
match the binomial quadratic expressions with their factored form.
tiles
$x^2 - 36$ $(x - 6)(x + 6)$ $x^2 + 16$ $(3x - 1)(3x + 1)$ $16x^2 + 9$ $4(x + 2)(x - 2)$
$9x^2 - 1$ $4x^2 - 16$
pairs
(three pairs of boxes with arrows between them)

Explanation:

Step1: Factor $x^2-36$

Use difference of squares: $a^2-b^2=(a-b)(a+b)$. Here $a=x$, $b=6$.
$x^2-36=(x-6)(x+6)$

Step2: Factor $9x^2-1$

Use difference of squares: $a^2-b^2=(a-b)(a+b)$. Here $a=3x$, $b=1$.
$9x^2-1=(3x-1)(3x+1)$

Step3: Factor $4x^2-16$

First factor out 4, then use difference of squares.
$4x^2-16=4(x^2-4)=4(x-2)(x+2)$

Step4: Identify non-factorable tiles

$x^2+16$ and $16x^2+9$ are sums of squares, cannot be factored over real numbers, so they are unused.

Answer:

$x^2 - 36 \longleftrightarrow (x - 6)(x + 6)$
$9x^2 - 1 \longleftrightarrow (3x - 1)(3x + 1)$
$4x^2 - 16 \longleftrightarrow 4(x + 2)(x - 2)$