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
boxes with arrows between them

Explanation:

Step1: Factor \(x^2 - 36\)

Using the difference of squares formula \(a^2 - b^2=(a - b)(a + b)\), here \(a = x\), \(b = 6\), so \(x^2-36=(x - 6)(x + 6)\).

Step2: Factor \(9x^2 - 1\)

Using the difference of squares formula \(a^2 - b^2=(a - b)(a + b)\), here \(a = 3x\), \(b = 1\), so \(9x^2-1=(3x - 1)(3x + 1)\).

Step3: Factor \(4x^2 - 16\)

First, factor out the common factor 4: \(4x^2-16 = 4(x^2 - 4)\). Then, using the difference of squares formula on \(x^2 - 4\) (where \(a=x\), \(b = 2\)), we get \(x^2-4=(x + 2)(x - 2)\). So, \(4x^2-16=4(x + 2)(x - 2)\).

Answer:

\(x^2 - 36\) pairs with \((x - 6)(x + 6)\)
\(9x^2 - 1\) pairs with \((3x - 1)(3x + 1)\)
\(4x^2 - 16\) pairs with \(4(x + 2)(x - 2)\)