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Simplify the expression. Write your answers using integers or improper fractions. 5(3u-5u-2)-(1)/(3)u Answer:

Simplify the expression. Write your answers using integers or improper fractions.\newline5(3u−5u−2)−13u 5(3 u-5 u-2)-\frac{1}{3} u \newlineAnswer:

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Full solution

Q. Simplify the expression. Write your answers using integers or improper fractions.\newline5(3u−5u−2)−13u 5(3 u-5 u-2)-\frac{1}{3} u \newlineAnswer:
  1. Distribute Terms: Distribute 55 into the terms inside the parentheses (3u−5u−2)(3u-5u-2). \newline5×3u=15u5 \times 3u = 15u\newline5×−5u=−25u5 \times -5u = -25u\newline5×−2=−105 \times -2 = -10\newlineSo, 5(3u−5u−2)5(3u-5u-2) becomes 15u−25u−1015u - 25u - 10.
  2. Combine Like Terms: Combine like terms from the result of the distribution.\newline15u−25u=−10u15u - 25u = -10u\newlineSo, 15u−25u−1015u - 25u - 10 becomes −10u−10-10u - 10.
  3. Write Entire Expression: Write down the entire expression with the combined like terms.\newlineThe expression now is −10u−10−13u-10u - 10 - \frac{1}{3}u.
  4. Combine Like Terms: Combine the like terms −10u-10u and −(1/3)u-(1/3)u. To combine these, we need a common denominator, which is 33. −10u-10u can be written as (−30/3)u(-30/3)u. So, (−30/3)u−(1/3)u=(−30−1)/3×u=(−31/3)u(-30/3)u - (1/3)u = (-30 - 1)/3 \times u = (-31/3)u.
  5. Write Simplified Expression: Write down the simplified expression with the combined like terms.\newlineThe expression now is (−313)u−10(-\frac{31}{3})u - 10.

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