Question

Please help!!!

I need help on the following problems...
Convert the product into a polynomial:

c.(–2ax^2+3ax–a^2)(–a^2x^2)




d. (6.3x^3y–3y^2–0.7x)·10x^2y^2




NOTE: The symbols such as ^ means exponents for the number to the right of it

Answer 1

c.
`2a^3x^4-3a^3x^3+a^4x^2`

d.
`63x^5y^3-30x^2y^4-7x^3y^2`

Explanation:

For this exercise you need to remember the following:

1. The multiplication of signs:

`(+)(+)=+\\(-)(-)=+\\(-)(+)=-`

2. The Product of powers property, which states that:

`(a^m)(a^n)=a^((m+n))`

3. The Distributive property:

`a(b\±c)=ab\±ac`

Knowing that, you can solve the multiplication of the polynomials:

c.
`(-2ax^2+3ax-a^2)(-a^2x^2)=\\\\=(-2ax^2)(-a^2x^2)+(3ax)(-a^2x^2)+(-a^2)(-a^2x^2)=2a^3x^4-3a^3x^3+a^4x^2`

d.
`(6.3x^3y-3y^2-0.7x)(10x^2y^2)=\\\\=(6.3x^3y)(10x^2y^2)+(-3y^2)(10x^2y^2)+(-0.7x)(10x^2y^2)=63x^5y^3-30x^2y^4-7x^3y^2`