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Which of the equations are true identities?
A.
n(n-2)(n+2)=n^(3)-4n
B.
(x+1)^(2)-2x+y^(2)=x^(2)+y^(2)+1
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? $\newline$ A. $n(n-2)(n+2)=n^{3}-4 n$ $\newline$ B. $(x+1)^{2}-2 x+y^{2}=x^{2}+y^{2}+1$ $\newline$ Choose $1$ answer: $\newline$ (A) Only A $\newline$ (B) Only B $\newline$ (C) Both A and B $\newline$ (D) Neither A nor B

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Full solution

Q. Which of the equations are true identities?

\newline

A.

n(n-2)(n+2)=n^{3}-4 n

\newline

B.

(x+1)^{2}-2 x+y^{2}=x^{2}+y^{2}+1

\newline

Choose

1

answer:

\newline

(A) Only A

\newline

(B) Only B

\newline

(C) Both A and B

\newline

(D) Neither A nor B

Expand A: Expand $A: n(n-2)(n+2)$ . $n(n^2 - 2n + 2n - 4) = n(n^2 - 4)$ .
Simplify expression: Simplify the expression. $n(n^2 - 4) = n^3 - 4n$ .
Check identity for $A$ : Check if $A$ is an identity. $n(n-2)(n+2) = n^3 - 4n$ is true.
Expand B: Expand B: $(x+1)^2 - 2x + y^2$ . $x^2 + 2x + 1 - 2x + y^2 = x^2 + y^2 + 1$ .
Check identity for B: Check if B is an identity. $\newline$ $(x+1)^2 - 2x + y^2 = x^2 + y^2 + 1$ is true.

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