Question

If 4x^2+20x+r=(2x+s)^2 for all values of x, what is the value of r-s?

Please help! & show work. thanks!

Answers

Expand (2x + s)2:

(2x + s)2 = (2x)2 + 2(2x)(s) + s2

? = 4x2 + 4sx + s2

This is to be identically equal to 4x2 + 20x + r. Therefore, we must have

4s = 20

s2 = r

From the first equation we immediately obtain s = 5. Substituting this into the second equation, we obtain r = 25. Then r - s = 25 - 5 = 20

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