Question

Please answer this question with steps

Answer 1

see explanation

Explanation:

`(1)/(3)` a³ -
`(3)/(4)` a² -
`(5)/(2)` - (
`(5)/(2)` a² +
`(3)/(2)` a³ +
`(a)/(3)` -
`(6)/(5)` ) ← distribute parenthesis by - 1

=
`(1)/(3)` a³ -
`(3)/(4)` a² -
`(5)/(2)` -
`(5)/(2)` a² -
`(3)/(2)` a³ -
`(a)/(3)` +
`(6)/(5)` ← collect like terms

= (
`(1)/(3)` a³ -
`(3)/(2)` a³ ) + (-
`(3)/(4)` a² -
`(5)/(2)` a² ) -
`(a)/(3)` + (-
`(5)/(2)` +
`(6)/(5)` ) ← change to common denominators

= (
`(2)/(6)` a³ -
`(9)/(6)` a³ ) + (-
`(3)/(4)` a² -
`(10)/(4)` a² ) -
`(a)/(3)` + (-
`(25)/(10)` +
`(12)/(10)` ) ← simplify

= -
`(7)/(6)` a³ -
`(13)/(4)` a² -
`(1)/(3)` a -
`(13)/(10)`

Answer 2

Explanation:

`\sf (1)/(3)a^3-(3)/(4)a^2-(5)/(2)-\left[(5)/(2)a^2+(3)/(2)a^3+(a)/(3)-(6)/(5)\right]=`

`\sf = (1)/(3)a^3-(3)/(4)a^2-(5)/(2)-(5)/(2)a^2-(3)/(2)a^3-(a)/(3)+(6)/(5)\\\\\\( Combine \ like \ terms)\\\\= (1)/(3)a^3 -(3)/(2)a^3 -(3)/(4)a^2-(5)/(2)a^2-(a)/(3)-(5)/(2)+(6)/(5)\\\\=\left[(1*2)/(3*2)-(3*3)/(2*3)\right]a^3 + \left[-(3)/(4)-(5*2)/(2*2)\right]a^2-(a)/(3)+\left[-(5*5)/(2*5)+(6*2)/(5*2)\right]\\\\\\`

`\sf ==\left[(2)/(6)-(9)/(6)\right]a^3+\left[-(3)/(4)-(10)/(4)\right]a^2-(a)/(3)+\left[-(25)/(10)+(12)/(10)\right]\\\\=(2-9)/(6)a^3+((-3-10))/(4)a^2-(a)/(3)+((-25+12))/(15)\\\\`

`\sf = (-7)/(6)a^3+ ((-13))/(4)a^2-(a)/(3)+((-13))/(15)\\\\=-(7)/(6)a^3-(13)/(4)a^2-(a)/(3)-(13)/(15)`