Given:
The expression
[tex](-2d^2+s)(5d^2-6s)[/tex]
To Find:
The product of the given expression.
Answer:
The product of the given expression is
[tex]-10d^4+17d^2s-6s^2[/tex]
Step-by-step explanation:
In the given expression, we must multiply term by term to get the product.
So, we begin by multiplying [tex]-2d^2[/tex] with [tex]5d^2[/tex] and [tex]-6s[/tex] and then [tex]s[/tex] with [tex]5d^2[/tex] and [tex]-6s[/tex].
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
[tex](d^2)(d^2)=d^4[/tex]
and
[tex](s)(s)=s^2[/tex]
Representing this mathematically, we see that
[tex](-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[/tex]
