Match the difference of squares with its factored form. Not all answer choices will be used. Reference Sheet - Difference of Two Squares (3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. x2−4 x2−36 4x2−100 The option "$\left(x+2\right)\left(x-2\right)$" (1 of 5) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.

Question

GPT-4o mini · Answer

To match the difference of squares with its factored form, let's break down each of the expressions you'd typically evaluate:

$x^2 - 4$: This can be factored as $(x + 2)(x - 2)$ since $4 = 2^2$.
$x^2 - 36$: This can be factored as $(x + 6)(x - 6)$ since $36 = 6^2$.
$4x^2 - 100$: First, we can factor out a 4, transforming it into $4(x^2 - 25)$. The expression $x^2 - 25$ can then be factored as $(x + 5)(x - 5)$, giving us $4(x + 5)(x - 5)$.

Now we can match the factored forms:

For $x^2 - 4$, the factored form is $(x + 2)(x - 2)$.
For $x^2 - 36$, the factored form is $(x + 6)(x - 6)$.
For $4x^2 - 100$, the factored form is $4(x + 5)(x - 5)$.

Based on this analysis, the matched responses would be:

$x^2 - 4$ → $(x + 2)(x - 2)$
$x^2 - 36$ → $(x + 6)(x - 6)$
$4x^2 - 100$ → $4(x + 5)(x - 5)$

Please let me know if you need further assistance!