Question

What is the product of `2x^2+7x-10` and `x+5` in standard form?

Answer 1

`2x^3 +17x^2+25x-50`

Explanation:

To begin, set up the expressions next to each other in parenthesis

`(x+5)(2x^2+7x-10)`

Now, you are going to distribute the first term in the first set of parenthesis throughout each term in the second set of parenthesis:

`(x+5)(2x^2+7x-10) =`

`=x(2x^2+7x-10) + 5(2x^2+7x-10)`

First, distribute `x` across `2x^2`, `7x`, and `-10`

So, multiply `x` by each of those terms to get:

`2x^3 +7x^2-10x`

Next, distribute the `5` throughout the set of parenthesis

`5(2x^2+7x-10)`

`=10x^2+35x-50`

Now add the 6 terms to get the final answer.

`2x^3 +7x^2-10x +10x^2+35x-50`

`=2x^3 +17x^2+25x-50`

Answer 2

=`2x^3+17x^2+25x-50`

Explanation:

A Product is the answer to a multiplication operation.

We have two expressions to multiply together:

`(x+5)(2x^2+7x -10)`

Each term in the first bracket must be multiplied by each term in the second bracket .

This gives: `(color(red)(x)color(blue)(+5))(2x^2+7x -10)`

=`color(red)(2x^3+7x^2-10x)color(blue)( +10x^2+35x-50)`

There are now 6 terms. Add the like terms together.

=`2x^3+17x^2+25x-50`