Question

Multiply the polynomials (7a – 7) and (2a2 – a + 5). Simplify the answer. Show your work.

Answer 1

Answer:
`=14a^3-21a^2+42a-35`

Explanation:

You can multiply the polynomials by applying the Distributive property.

It is important to remember the Product of powers property, which states that:

`(b^a)(b^c)=b^{(a+c)`

Where b is the base and a and c are exponents.

It is also important to remember the multiplication of signs:

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

Then:

Each term inside of the first parentheses must multiply each term inside of the second parentheses:

`(7a-7)(2a^2-a+5)=(7a)(2a^2)+(7a)(-a)+(7a)(5)+(-7)(2a^2)+(-7)(-a)+(-7)(5)\\\\=14a^3-7a^2+35a-14a^2+7a-35`

Finally, add like terms:

`=14a^3-21a^2+42a-35`