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# Interpreting nonlinear expressions — Harder example

Watch Sal work through a harder Interpreting nonlinear expressions problem.

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• I have my SAT tomorrow and I am reviewing some math. How is 64 distributed. I know you explained this in a previous comment, but if you look closely, d is not being distributed. Therefore, if you are multiplying d by 64, why is it necessary to distribute every number by 64 if it was not original apart of the distributive property.
• If 4d^3 = (4^3)(d^3), then it amounts to 64d^3. 64 is distributed because the equation is 3.98*10^-20*64d^3. All terms are being multiplied by 64, so it can be factored. Sorry that your question wasn't answered until now! :(
• Doesn't factoring out the 64 imply that the the 64 is multiplied by every term in the parentheses?
• You don't have to do this in this specific case because we just have to see how many times longer Mar's revolution time would be compared to that of Mercury's. We just have to see that one value which shows how much longer the revolution would take (8). Multiplying 64 with every single term in the parentheses (after finding the principal root which is done near ) would just add an extra step. Remember, the SAT is time constrained, so the quickest option should be used!
• Isn't 6% 0.06? Then why did you consider that it is 1.06 in Interpreting nonlinear expressions — Harder example?
• 6% is indeed .06, but that's not all the question asks you for. Instead, the answer choices describe "an increase of 6%". To put that into math, it's the original price plus 6% of what it was:
x + .06x = x(1.06)
That's how we get 1.06 for the 6% increase, and why it's in there instead of plain .06. If the function was 10000(.06)^(q/4), it would mean that the styling service only retains 6% of its subscribers per year, or that it loses 94% every year.
• Hi! I have a question... I don't understand how you would square root the whole equation after you substitute the number 4 into d (for distance)? Can someone please explain it to me? Thank you in advance! xx
• What kind of topics are there in sat
• The Math SAT has 3 major categories: Heart of Algebra, Problem Solving and Data Analysis, and Passport to Advanced Math.

See the CollegeBoard website for a more detailed explanation.

Sal covers all these topics in the videos provided.
• It says 4 times as distant from the sun as Mercury is, and the distance is d^3. Why is (4d)^3 instead of 4(d^3)?
• I'm not sure, but since the distance of Mercury is represented by d, you multiply 4 by d, and also by the exponent. The exponent remains 3.
• Can anybody explain me that q/4 how its not 1 quarter? I am utterly confused
• If we have q = 1 it means it is one quarter. When it is q = 4 its is one whole year as in one year we have 4 quarter
• Why is 64 written outside of the parentheses?
(1 vote)
• It is the associative property: you can regroup multiplication without changing the resulting product.
a ∙ b = (a)b = ab = a(b)
If you want to take a LOT of unnecessary time on this SAT problem, you can multiply it into the inside of the parentheses, but it is much much much faster to use the associative property and keep that number separate.
• How did you get 8? I understand that you got it from the square root of 64, but how can that determine the time it will take Mars to evolve around the sun? Wouldn't all the factors of the equation be needed?