Factor $$ 32 x^{2}-50 $$ None of these $$ \begin{array}{l} ext { O2 }(4 x-5)^{2} \ 2(4 x-5)(4 x+5) \ (8 x-5)(8 x+5)\end{array} $$

Question

Factor $$ 32 x^{2}-50 $$ None of these $$ \begin{array}{l}	ext { O2 }(4 x-5)^{2} \ 2(4 x-5)(4 x+5) \ (8 x-5)(8 x+5)\end{array} $$

UpStudy AI · Accepted Answer

We start with the expression:
$$
32x^2 - 50
$$

**Step 1. Factor out the greatest common factor (GCF):**

Both terms are divisible by $$2$$:
$$
32x^2 - 50 = 2(16x^2 - 25)
$$

**Step 2. Recognize the difference of squares:**

Notice that $$16x^2 - 25$$ is a difference of squares since:
$$
16x^2 = (4x)^2 \quad \text{and} \quad 25 = 5^2
$$
Thus we can write:
$$
16x^2 - 25 = (4x)^2 - 5^2
$$

**Step 3. Factor the difference of squares:**

Using the formula $$a^2 - b^2 = (a - b)(a + b)$$ with $$a = 4x$$ and $$b = 5$$:
$$
(4x)^2 - 5^2 = (4x - 5)(4x + 5)
$$

**Step 4. Combine the factors:**

Substitute back into the expression:
$$
2(16x^2 - 25) = 2(4x - 5)(4x + 5)
$$

Thus, the factorization of $$32x^2 - 50$$ is:
$$
2(4x-5)(4x+5)
$$

Among the given options, the correct factorization is:
$$
2(4x-5)(4x+5)
$$
The factorization of $$32x^2 - 50$$ is $$2(4x-5)(4x+5)$$.

Factor \( 32 x^{2}-50 \) None of these \( \begin{array}{l}\text { O2 }(4 x-5)^{2} \\ 2(4 x-5)(4 x+5) \\ (8 x-5)(8 x+5)\end{array} \)

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