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Simplify to create an equivalent expression. 5(10 k+1)+2(2+8k) Choose 1 answer: (A) 66 k+9 (B) 64 k+9 (c) 66 k+54 (D) 64 k-9

Simplify to create an equivalent expression.\newline5(10k+1)+2(2+8k)5(10k+1)+2(2+8k)\newlineChoose 11 answer:\newline(A) 66k+966k+9\newline(B) 64k+964k+9\newline(C) 66k+5466k+54\newline(D) 64k−964k-9

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Full solution

Q. Simplify to create an equivalent expression.\newline5(10k+1)+2(2+8k)5(10k+1)+2(2+8k)\newlineChoose 11 answer:\newline(A) 66k+966k+9\newline(B) 64k+964k+9\newline(C) 66k+5466k+54\newline(D) 64k−964k-9
  1. Distribute Multiplication: First, we need to distribute the multiplication over addition in both expressions. For the first expression, we multiply 55 by both 10k10k and 11. For the second expression, we multiply 22 by both 22 and 8k8k.
  2. Distribute 55 over (10k+1)(10k + 1): Distribute 55 over (10k+1)(10k + 1):5×10k+5×1=50k+55 \times 10k + 5 \times 1 = 50k + 5
  3. Distribute 22 over (2+8k)(2 + 8k): Distribute 22 over (2+8k)(2 + 8k):2×2+2×8k=4+16k2 \times 2 + 2 \times 8k = 4 + 16k
  4. Add Distributed Results: Now, we add the results of the distributions together: 50k+550k + 5 + 4+16k4 + 16k
  5. Combine Like Terms: Combine like terms 50k50k and 16k16k and 55 and 44:50k+16k+5+4=66k+950k + 16k + 5 + 4 = 66k + 9

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