Dear Sir or Madam;
My daughter has a math problem that I can't help her with. The problem is 21+2[3z+5(3z+8)] I can get the answer 101 +36z but I can't show her the correct way to write it out. Would you please show the correct way to show her work...

Thank you in advance

Dennis Dyer (Father)

Hi Dennis,

To simplify the expression 21+2[3z+5(3z+8)] you need to approach it from "the inside out". This expression has parentheses, ( ), nested "inside" square brackets, [ ], so working from the "inside out" start with (3z+8).

5(3z+8) = 5x3z+5x8 = 15z+40.

Thus the expression inside the square brackets becomes

3z+5(3z+8) = 3z+15z+40 = 18z+40

Now working your way outside the square brackets

2[3z+5(3z+8)] = 2[18z+40] = 2x18z+2x40 = 36z+80

The last step is to add 21 to get

21+2[3z+5(3z+8)] = 21+36z+80 = 36z+101

This has much more detail then I would include as a solution. If asked to simplify 21+2[3z+5(3z+8)] my solution would be:

 21+2[3z+5(3z+8)] = 21+2[3z+15z+40] = 21+2[18z+40] = 21+36z+80 = 36z+101
Cheers,
Penny
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