Question

What is the standard form of `y= (2x^2 + 2)(x + 5)(x -1)^2`?

Answer 1

`2x^5 + 8x^4 - 16x^3 +1 6x^2 - 18x + 10`

Explanation:

Expand the 2 'pairs' of brackets

ie `(2x^2 + 2)(x + 5 ) and (x - 1 )(x - 1 )`

using the FOIL method on each pair to obtain :

`(2x^3 + 10x^2 + 2x + 10 )(x^2 - x - x + 1 )`

`= (2x^3 + 10x^2 + 2x + 10)( x^2 - 2x + 1 )`

Now each term in the 2nd bracket must be multiplied by each
term in the 1st.

ie `2x^3(x^2 -2x + 1) + 10x^2(x^2 - 2x + 1 ) + 2x(x^2 - 2x + 1 )`

`+ 10(x^2 - 2x + 1 )`

`= 2x^5 - 2x^4 + 2x^3 + 10x^4 - 20x^3 + 10x^2 + 2x^3 - 4x^2`

`+ 2x + 10x^2 - 20x + 10`

now collect 'like terms'

`= 2x^5 + 8x^4 - 16x^3 + 16x^2 - 18x + 10`