identify the mistake and solve correctly.

Question

A student submitted the following problem but the solution is incorrect. • Identify the mistake. What did the student do wrong? • Solve the problem correctly. Sec. 12.5 #72 Subtract (a5 – 1 3 a3 – 5a) from ( 3 4 a5 + 1 2 a4 + 6a). Incorrect solution: (a5 – 1 3 a3 – 5a) - ( 3 4 a5 + 1 2 a4 + 6a) a5 – 1 3 a3 – 5a - 3 4 a5 - 1 2 a4 - 6a 1 4 a5 - 1 2 a4 – 1 3 a3 -11a

Answer 1

Here's the correct solution:

Original expression: (a^5 - (1/3)a^3 - 5a) - (3/4)a^5 - (1/2)a^4 - 6a

Distribute the negative sign: = a^5 - (1/3)a^3 - 5a - (3/4)a^5 + (1/2)a^4 + 6a

Now, combine like terms: = (a^5 - (3/4)a^5) - (1/3)a^3 + (1/2)a^4 - 5a + 6a

= (1/4)a^5 - (1/3)a^3 + (1/2)a^4 + a

So, the correct solution is: (1/4)a^5 - (1/3)a^3 + (1/2)a^4 + a

Answer 2

The student mixed up what was being subtracted from

34a⁵+12a⁴+ 0a³+6a

-( a⁵ -13a³ -5a)

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33a⁵+12a⁴+13a³+11a