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Julias work to find the difference of (6p^2 - 8) - (7p + 5 + 5p^2)

Given: (6p^2 - 8) - (7p + 5 + 5p^2)
Step 1: 6p^2 - 8 - 7p + 5 + 5p^2
Step 2: 6p^2 + 5p^2 - 7p - 8 + 5
Step 3: 11p^2 - 7p - 3
Complete the statements.
Julia ____. (choices are correctly found the difference of the polynomials, first made an error in Step 1, first made an error in Step 2, or first made an error in Step 3.) The difference of (6p^2 - 8) - (7p + 5 + 5p^2) is ____ (choices are 11p^2 - 7p - 3, 11p^2 + 7p - 3, p^2 - 7p - 13, or p^2 + 7p - 13)

1 answer

Julia first made an error in Step 1.

In Step 1, she should have correctly expressed the subtraction of the polynomial. The expression \( (6p^2 - 8) - (7p + 5 + 5p^2) \) becomes \( 6p^2 - 8 - 7p - 5 - 5p^2 \).

Combining terms correctly, we have:

  1. \( 6p^2 - 5p^2 = 1p^2 \)
  2. The \( -7p \) term remains as is.
  3. The constant terms yield \( -8 - 5 = -13 \).

So the correct simplified polynomial is \( p^2 - 7p - 13 \).

Therefore, the difference of \( (6p^2 - 8) - (7p + 5 + 5p^2) \) is p^2 - 7p - 13.