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: pairs section with boxes and arrows, image content omitted

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, \(a = 3x\), \(b = 1\). So \(9x^2 - 1=(3x - 1)(3x + 1)\).

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

First, factor out the common factor 4: \(4(x^2 - 4)\). Then use the difference of squares on \(x^2 - 4\) (\(a = x\), \(b = 2\)): \(4(x - 2)(x + 2)=4(x + 2)(x - 2)\).

Answer:

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