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Select the expressions that are equivalent to 4(4n+1)+5n. {:[9n+4],[(4n+1)4+5n],[1(4n+4)+5n],[4n+21]:}

Select the expressions that are equivalent to 4(4n+1)+5n 4(4 n+1)+5 n .\newline9n+4(4n+1)4+5n1(4n+4)+5n4n+21 \begin{array}{c} 9 n+4 \\ (4 n+1) 4+5 n \\ 1(4 n+4)+5 n \\ 4 n+21 \end{array}

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Full solution

Q. Select the expressions that are equivalent to 4(4n+1)+5n 4(4 n+1)+5 n .\newline9n+4(4n+1)4+5n1(4n+4)+5n4n+21 \begin{array}{c} 9 n+4 \\ (4 n+1) 4+5 n \\ 1(4 n+4)+5 n \\ 4 n+21 \end{array}
  1. Simplify Expression: Simplify the given expression 4(4n+1)+5n4(4n+1)+5n.\newlineCalculation: 4(4n)+4(1)+5n=16n+4+5n=21n+44(4n) + 4(1) + 5n = 16n + 4 + 5n = 21n + 4.
  2. Compare with Choices: Compare the simplified expression 21n+421n + 4 with each choice.\newlineCalculation: \newline- 9n+49n + 4 is not equivalent to 21n+421n + 4.\newline- (4n+1)4+5n(4n+1)4 + 5n simplifies to 16n+4+5n=21n+416n + 4 + 5n = 21n + 4, which is equivalent.\newline- 1(4n+4)+5n1(4n+4) + 5n simplifies to 4n+4+5n=9n+44n + 4 + 5n = 9n + 4, which is not equivalent.\newline- 4n+214n + 21 is not equivalent to 21n+421n + 4.

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