drag the tiles to the boxes to form correct pairs. not all tiles will be used. match each binomial with its…

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 have (16x^{2}-1=(4x)^{2}-1^{2}), so (16x^{2}-1=(4x - 1)(4x + 1)).

Step3: Factor (16x^{2}-4)

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

Step4: Factor (4x^{2}-1)

Using the difference - of - squares formula with (a = 2x) and (b = 1), we have (4x^{2}-1=(2x + 1)(2x - 1)).

Step5: Factor (4x^{2}-9)

We have (4x^{2}-9=(2x)^{2}-3^{2}), so (4x^{2}-9=(2x + 3)(2x - 3)). And (16x^{2}+1) cannot be factored over the real numbers using real - valued binomials.

Answer:

(16x^{2}-1\longleftrightarrow(4x - 1)(4x + 1)) (16x^{2}-4\longleftrightarrow4(2x + 1)(2x - 1)) (4x^{2}-1\longleftrightarrow(2x + 1)(2x - 1)) (4x^{2}-9\longleftrightarrow(2x + 3)(2x - 3))