How did you factor our r

Mathematics

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Step-by-step solution

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Okay, Samadhi, let's break down how rr was factored out from the equation.

We had the equation:

260=2r+8821r260 = 2r + \frac{88}{21} r

Factoring means identifying a common term that appears in multiple parts of an expression and writing the expression as the product of that common term and the sum/difference of the remaining parts.

In the expression 2r+8821r2r + \frac{88}{21} r, the variable rr is present in both terms (2r2r and 8821r\frac{88}{21} r).

  1. Identify the common factor.

    The common factor is rr.

  2. Rewrite each term as a product involving the common factor.

    • The first term, 2r2r, can be written as r×2r \times 2.
    • The second term, 8821r\frac{88}{21} r, can be written as r×8821r \times \frac{88}{21}.
  3. Apply the distributive property in reverse.

    The distributive property states that a(b+c)=ab+aca(b+c) = ab + ac.
    We have r×2+r×8821r \times 2 + r \times \frac{88}{21}.
    Comparing this to ab+acab + ac, we can see that a=ra=r, b=2b=2, and c=8821c=\frac{88}{21}.
    So, we can rewrite it as r(2+8821)r \left(2 + \frac{88}{21}\right).

    Therefore, the equation becomes:

    260=r(2+8821)260 = r \left(2 + \frac{88}{21}\right)

    This is how rr was factored out.

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