Question

What is the product?

Answer 1

Given:

The expression

`(-2d^2+s)(5d^2-6s)`

To Find:

The product of the given expression.

Answer:

The product of the given expression is

`-10d^4+17d^2s-6s^2`

Explanation:

In the given expression, we must multiply term by term to get the product.

So, we begin by multiplying
`-2d^2` with
`5d^2` and
`-6s` and then
`s` with
`5d^2` and
`-6s`.

We then take the sum of the four different terms we get, keeping in mind that the product of two minus signs (-) will be a positive (+).

Moreover, using the laws of exponents, we will have

`(d^2)(d^2)=d^4`

and

`(s)(s)=s^2`

Representing this mathematically, we see that

`(-2d^2+s)(5d^2-6s)\\\\=(-2d^2)(5d^2-6s)+(s)(5d^2-6s)\\\\=(-2d^2)(5d^2)+(-2d^2)(-6s)+(s)(5d^2)+(s)(-6s)\\\\=-10d^4+12d^2s+5d^2s-6s^2\\\\=-10d^4+17d^2s-6s^2`