Question

Question #c7477

Answer 1

`2x^4+16x^3+35x^2+10x-21`

Explanation:

In problems like these, we have to multiply everything in the first set of parentheses by everything in the second parenthesis.

`color(blue)(x^2)+color(red)(6x)+color(orange)(7)`

`color(blue)(x^2)(2x^2+4x-3)+color(red)(6x)(2x^2+4x-3)+color(orange)(7)(2x^2+4x-3)`

Distributing the `color(blue)(x^2)`:
`2x^4+4x^3-3x^2`

Distributing the `color(red)(6x)`:
`12x^3+24x^2-18x`

Distributing the `color(orange)(7)`:
`14x^2+28x-21`

Putting it all together:
`2x^4+4x^3-3x^2+12x^3+24x^2-18x+14x^2+28x-21`

Combining like terms:

`2x^4+16x^3+35x^2+10x-21`