j^(3)+3j^(2)k+3jk^(2)+k^(3) Which of the following is equivalent to the given expression? Choose 1 answer: (A) j^(3)+3(jk)^(2)+k^(3) (B) j^(3)+6(jk)^(2)+k^(3) (C) j^(3)+3jk(j+k)+k^(3) (D) j^(3)+6jk(j+k)+k^(3)

Recognize Pattern: Recognize the pattern in the given expression, it looks like a binomial expansion of (j+k)^3.Expand Expression: Expand (j+k)^3 to check if it matches the given expression. (j+k)^3 = j^3 + 3j^2k + 3jk^2 + k^3Compare with Choices: Compare the expanded form with the answer choices. The expanded form matches with answer choice (A) j^(3)+3(jk)^(2)+k^(3).Identify Mistake: Realize there's a mistake in the previous step; 3(jk)^(2) is actually 3j^2k^2, not 3j^2k + 3jk^2.

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$j^{3}+3j^{2}k+3jk^{2}+k^{3}$ $\newline$ Which of the following is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $j^{3}+3(jk)^{2}+k^{3}$ $\newline$ (B) $j^{3}+6(jk)^{2}+k^{3}$ $\newline$ (C) $j^{3}+3jk(j+k)+k^{3}$ $\newline$ (D) $j^{3}+6jk(j+k)+k^{3}$

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Calculus

Find derivatives of using multiple formulae

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j^{3}+3j^{2}k+3jk^{2}+k^{3}

\newline

Which of the following is equivalent to the given expression?

\newline

Choose

1

answer:

\newline

(A)

j^{3}+3(jk)^{2}+k^{3}

\newline

(B)

j^{3}+6(jk)^{2}+k^{3}

\newline

(C)

j^{3}+3jk(j+k)+k^{3}

\newline

(D)

j^{3}+6jk(j+k)+k^{3}

Recognize Pattern: Recognize the pattern in the given expression, it looks like a binomial expansion of $(j+k)^3$ .
Expand Expression: Expand $(j+k)^3$ to check if it matches the given expression. $\newline$ $(j+k)^3 = j^3 + 3j^2k + 3jk^2 + k^3$
Compare with Choices: Compare the expanded form with the answer choices. $\newline$ The expanded form matches with answer choice (A) $j^{3}+3(jk)^{2}+k^{3}$ .
Identify Mistake: Realize there's a mistake in the previous step; $3(jk)^{2}$ is actually $3j^{2}k^{2}$ , not $3j^{2}k + 3jk^{2}$ .