Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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?\newlineA. n(n2)(n+2)=n34n n(n-2)(n+2)=n^{3}-4 n \newlineB. (x+1)22x+y2=x2+y2+1 (x+1)^{2}-2 x+y^{2}=x^{2}+y^{2}+1 \newlineChoose 11 answer:\newline(A) Only A\newline(B) Only B\newline(C) Both A and B\newline(D) Neither A nor B

Full solution

Q. Which of the equations are true identities?\newlineA. n(n2)(n+2)=n34n n(n-2)(n+2)=n^{3}-4 n \newlineB. (x+1)22x+y2=x2+y2+1 (x+1)^{2}-2 x+y^{2}=x^{2}+y^{2}+1 \newlineChoose 11 answer:\newline(A) Only A\newline(B) Only B\newline(C) Both A and B\newline(D) Neither A nor B
  1. Expand A: Expand A:n(n2)(n+2)A: n(n-2)(n+2).n(n22n+2n4)=n(n24)n(n^2 - 2n + 2n - 4) = n(n^2 - 4).
  2. Simplify expression: Simplify the expression. n(n24)=n34nn(n^2 - 4) = n^3 - 4n.
  3. Check identity for AA: Check if AA is an identity.n(n2)(n+2)=n34nn(n-2)(n+2) = n^3 - 4n is true.
  4. Expand B: Expand B: (x+1)22x+y2(x+1)^2 - 2x + y^2.x2+2x+12x+y2=x2+y2+1x^2 + 2x + 1 - 2x + y^2 = x^2 + y^2 + 1.
  5. Check identity for B: Check if B is an identity.\newline(x+1)22x+y2=x2+y2+1(x+1)^2 - 2x + y^2 = x^2 + y^2 + 1 is true.

More problems from Power rule