Did I factor this correctly this time.
4x^2+8x+4
(2x+2) (2x+2)
Yes...work backwords to check your answer
Can you help me with this particular question:
Like us, Liebniz (and Newton with different notation) might write an equation such as dy=4dx. As the textbook notes, the problem with the seventeenth century calculus is that it is not clear what the symbols dy and dx meant. Sometimes they represented finite quantities, sometimes quantities that were non-zero, but smaller than anything else (infinitesimal). Explain what such an equation means today, using the concept of limit. (You may use as an example, the function y= x squared at x=2. Compute the relationship between the change in y and change in x for very small changes in x above 2, and then illustrate a limit process that establishes the equation dy=4dx.)
To determine if you factored the quadratic expression correctly, you can expand the factored form to see if it simplifies back to the original expression.
Let's expand (2x+2)(2x+2) using the distributive property:
(2x + 2)(2x + 2) = 2x(2x) + 2x(2) + 2(2x) + 2(2)
Now simplify each term:
= 4x^2 + 4x + 4x + 4
Combine like terms:
= 4x^2 + 8x + 4
As you can see, the expanded form of (2x+2)(2x+2) is indeed equal to the original expression 4x^2 + 8x + 4. Therefore, you have correctly factored the expression as (2x+2)(2x+2).