F) Factor completely. $$ 4 k^{2}-100 $$

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UpStudy AI · Accepted Answer

1. Recognize that the expression can be factored by first factoring out the greatest common factor:
   $$
   4 k^{2}-100=4\left(k^{2}-25\right)
   $$

2. Notice that $$k^{2}-25$$ is a difference of two squares. Recall the formula:
   $$
   a^{2}-b^{2}=(a-b)(a+b)
   $$
   Here, we have $$a=k$$ and $$b=5$$, so:
   $$
   k^{2}-25 = (k-5)(k+5)
   $$

3. Substitute back into the expression:
   $$
   4(k^{2}-25)=4(k-5)(k+5)
   $$

Thus, the fully factored form is:
$$
4(k-5)(k+5)
$$
The expression $$4k^{2}-100$$ can be factored completely as $$4(k-5)(k+5)$$.

F) Factor completely.

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