Question

for In the given​ expression, calculate as indicated. Express your answer as a single polynomial in standard form. 4x^(3)-2x^(2)+9)-(6x^(2)-6x+5), what is the answer

Answer 1

The polynomial in standard form is
`y = 14 + 6\cdot x - 8\cdot x^(2)+4\cdot x^(3)`.

Explanation:

A polynomial in standard fulfills the following condition:

`y = \Sigma_(i=0)^(m)\,c_(i)\cdot x^(i)`,
`\forall\,i\in \mathbb{N}`,
`0 \leq i \leq m`

Let be
`y = (4\cdot x^(3)-2\cdot x^(2)+9)-(6\cdot x^(2)-6\cdot x + 5)`, which is now handled algebraically:

1)
`(4\cdot x^(3)-2\cdot x^(2)+9)-(6\cdot x^(2)-6\cdot x + 5)` Given

2)
`(4\cdot x^(3)-2\cdot x^(2)+9) +(-1)\cdot (6\cdot x^(2)-6\cdot x + 5)`
`(-1)\cdot a = -a`

3)
`(4\cdot x^(3)-2\cdot x^(2)+9) +[(-1)\cdot (6\cdot x^(2))+(-6\cdot x)\cdot (-1)+5]` Definition of substraction/Distributive property

4)
`(4\cdot x^(3)-2\cdot x^(2)+9)+(-6\cdot x^(2)+6\cdot x + 5)`
`(-1)\cdot a = -a`/
`(-a)\cdot (-b) = a\cdot b`

5)
`4\cdot x^(3)+ (-2\cdot x^(2)-6\cdot x^(2))+6\cdot x + (9+5)` Associative and commutative properties

6)
`4\cdot x^(3)-8\cdot x^(2)+6\cdot x + 14` Distributive property/Definition of addition

7)
`14 + 6\cdot x -8\cdot x^(2)+4\cdot x^(3)` Commutative property/Result

The polynomial in standard form is
`y = 14 + 6\cdot x - 8\cdot x^(2)+4\cdot x^(3)`.