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What does rs + 2 mean?

Mathematics

ScanSolve AI Answer

Answer

C

Multiply rr by ss, then add 2

Step-by-step solution

5 steps

here are the solutions to the questions:

Part 1· 2 steps

What does rs+2rs + 2 mean?

  1. Interpret the term rsrs.

    In algebra, when two variables are written next to each other, it implies multiplication. So, rsrs means r×sr \times s.

  2. Interpret the entire expression rs+2rs + 2.

    This means that after multiplying rr by ss, you then add 2 to the result.
    Comparing this to the options:
    A. Multiply rr and ss by 2 (Incorrect, this would be 2rs2rs or 2(r+s)2(r+s))
    B. Add rr to ss, then add 2 (Incorrect, this would be (r+s)+2(r+s)+2)
    C. Multiply rr by ss, then add 2 (Correct)
    D. Add 2 to ss, then multiply by rr (Incorrect, this would be r(s+2)r(s+2))

    The correct option is C. Multiply rr by ss, then add 2.

Part 2· 3 steps

Simplify: 3p2+2p+2p2+p3p^2 + 2p + 2p^2 + p?

  1. Identify and group like terms.

    Like terms have the same variable(s) raised to the same power.
    The terms with p2p^2 are 3p23p^2 and 2p22p^2.
    The terms with pp are 2p2p and pp (which is 1p1p).

  2. Combine the like terms.

    For the p2p^2 terms:

    3p2+2p2=(3+2)p2=5p23p^2 + 2p^2 = (3+2)p^2 = 5p^2

    For the pp terms:

    2p+p=(2+1)p=3p2p + p = (2+1)p = 3p
  3. Write the simplified expression by combining the results from Step 2.

    5p2+3p5p^2 + 3p

    Comparing this to the options:
    A. 8p28p^2 (Incorrect)
    B. 8p68p^6 (Incorrect)
    C. 5p2+3p5p^2 + 3p (Correct)
    D. 7p2+p7p^2 + p (Incorrect)

    The correct option is C. 5p2+3p5p^2 + 3p.

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