Question #c7477

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Answer 1 · 2018-02-13T00:15:56

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

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:

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