Question

drag the tiles to the boxes to form correct pairs. not all tiles will be used. match each binomial with its factors. 16x² - 1 (2x + 1)(2x - 1) 16x² - 4 (2x + 3)(2x - 3) 16x² + 1 4(2x + 1)(2x - 1) 4x² - 1 (4x - 1)(4x + 1) 4x² - 9

Explanation:

Step1: Recall difference - of - squares formula

The difference - of - squares formula is \(a^{2}-b^{2}=(a + b)(a - b)\).

Step2: Factor \(16x^{2}-1\)

We can rewrite \(16x^{2}-1\) as \((4x)^{2}-1^{2}\). Using the difference - of - squares formula, we get \((4x + 1)(4x - 1)\).

Step3: Note \(16x^{2}+1\)

\(16x^{2}+1\) cannot be factored over the real numbers using real - valued binomial factors.

Step4: Factor \(4x^{2}-9\)

Rewrite \(4x^{2}-9\) as \((2x)^{2}-3^{2}\). By the difference - of - squares formula, it factors to \((2x + 3)(2x - 3)\).

Step5: Factor \(16x^{2}-4\)

First, factor out the common factor 4: \(16x^{2}-4 = 4(4x^{2}-1)\). Then factor \(4x^{2}-1=(2x + 1)(2x - 1)\), so \(16x^{2}-4=4(2x + 1)(2x - 1)\).

Step6: Factor \(4x^{2}-1\)

Rewrite \(4x^{2}-1\) as \((2x)^{2}-1^{2}\). Using the difference - of - squares formula, we get \((2x + 1)(2x - 1)\).

Answer:

\(16x^{2}-1\) - \((4x - 1)(4x + 1)\)
\(16x^{2}+1\) - No real - valued binomial factors
\(4x^{2}-9\) - \((2x + 3)(2x - 3)\)
\(16x^{2}-4\) - \(4(2x + 1)(2x - 1)\)
\(4x^{2}-1\) - \((2x + 1)(2x - 1)\)