Question

What is the standard form of `y= (x+x^2)(6x-3) -(2x+2)^3`?

Answer 1

See explanation...

Explanation:

`y=(x+x^2)(6x-3)-(2x+2)^3`

Multiply `x+x^2` and `6x-3` using Foil method

So,
`(x+x^2)(6x-3)=6x^2-3x+6x^3-3x^2=3x^2-3x+6x^3`

To,simplify `(2x+2)^3` Use the formula(Binomial expansion) `a^3+3a^2b+3ab^2+b^3`

`(2x+2)^3=8x^3+24x^2+24x+8`

Watch this video to now about the binomial expansion:

So,

`y=(3x^2-3x+6x^3)-(8x^3+24x^2+24x+8)`

Change the signs,

`rarry=3x^2-3x+6x^3-8x^3-24x^2-24x-8`

`rarry=-21x^2-3x+6x^3-8x^3-24x-8`

`rarry=-21x^2-27x+6x^3-8x^3-8`

`rarry=-21x^2-27x-2x^3-8`

In Standard form:

`rarry=-2x^3-21x^2-27x-8`