Question

explain step by step how to use the horizontal method to multiply the two polynomialsthe two polynomials are in the photo—>

Answer 1

The horizontal method involves multiplying each term of the first polynomial times each term of the second polynomial.

Given:

`(3a^2+5a-2)(5a^2\text{ -3a + 4)}`

Multiplying the two terms:

`\begin{gathered} =(3a^2+5a-2)(5a^2\text{ -3a + 4)} \\ =3a^2(5a^2-3a+4)+5a(5a^2-3a+4)-2(5a^2-3a\text{ +4)} \\ =15a^4-9a^3+12a^2+25a^3-15a^2+20a-10a^2\text{ + 6a - 8} \end{gathered}`

Collect like terms:

`\begin{gathered} =15a^4-9a^3+25a^3+12a^2-15a^2-10a^2\text{ + 20a + 6a - 8} \\ =15a^4+16a^3-13a^2\text{ + 26a -8} \end{gathered}`

Answer:

`=15a^4+16a^3-13a^2\text{ + 26a -8}`