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Which of the equations are true identities?
A. 
n^(3)+3n^(2)+2n=n(n+1)(n+2)
B. 
(a+3)^(2)-9=a^(2)+6a
Choose 1 answer:
(A) Only A
(B) Only B
(C) Both 
A and 
B
(D) Neither A nor B

Which of the equations are true identities?\newlineA. n3+3n2+2n=n(n+1)(n+2) n^{3}+3 n^{2}+2 n=n(n+1)(n+2) \newlineB. (a+3)29=a2+6a (a+3)^{2}-9=a^{2}+6 a \newlineChoose 11 answer:\newline(A) Only A\newline(B) Only B\newline(C) Both A \mathrm{A} and B \mathrm{B} \newline(D) Neither A nor B

Full solution

Q. Which of the equations are true identities?\newlineA. n3+3n2+2n=n(n+1)(n+2) n^{3}+3 n^{2}+2 n=n(n+1)(n+2) \newlineB. (a+3)29=a2+6a (a+3)^{2}-9=a^{2}+6 a \newlineChoose 11 answer:\newline(A) Only A\newline(B) Only B\newline(C) Both A \mathrm{A} and B \mathrm{B} \newline(D) Neither A nor B
  1. Expand Equation A: Let's expand the right side of equation A and see if it matches the left side.\newlinen(n+1)(n+2)=n(n2+3n+2)=n3+3n2+2nn(n+1)(n+2) = n(n^2 + 3n + 2) = n^3 + 3n^2 + 2n
  2. Check Equation B: Now let's check equation B by expanding the left side.\newline(a+3)29=a2+6a+99=a2+6a(a+3)^2 - 9 = a^2 + 6a + 9 - 9 = a^2 + 6a
  3. Verify Identities: Both equations AA and BB seem to be true identities after expanding and simplifying.

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