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Select the expressions that are equivalent to 9(5z)9(5z).\newlineMulti-select Choices:\newline(A) z(9×5)z(9 \times 5)\newline(B) 9+5z9 + 5z\newline(C) z+14z + 14\newline(D) (z+5)9(z + 5)9

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Full solution

Q. Select the expressions that are equivalent to 9(5z)9(5z).\newlineMulti-select Choices:\newline(A) z(9×5)z(9 \times 5)\newline(B) 9+5z9 + 5z\newline(C) z+14z + 14\newline(D) (z+5)9(z + 5)9
  1. Simplify expression: Step 11: Simplify the given expression 9(5z)9(5z).\newlineCalculation: 9×5z=45z9 \times 5z = 45z.
  2. Compare with choices: Step 22: Compare the simplified expression with each choice. \newline(A) z(9×5)z(9 \times 5) simplifies to z×45=45zz \times 45 = 45z.
  3. Check choice (B): Step 33: Check choice (B) 9+5z9 + 5z.\newlineCalculation: This expression cannot be simplified to match 45z45z.
  4. Check choice (C): Step 44: Check choice (C) z+14z + 14.\newlineCalculation: This expression cannot be simplified to match 45z45z.
  5. Check choice (D): Step 55: Check choice (D) z + 5)9\. Calculation: Distribute \$9 to get 9z+459z + 45, which does not simplify to 45z45z.

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