Multiplication. Polynomials by Monomials.

86. Multiplication. Polynomials by Monomials.

We have for positive numbers (§ 39),

The same law holds for negative numbers.

multiply a polynomial by a monomial, therefore,

Multiply each term of the polynomial by the monomial, and add the partial products.

1. Find the product of $ab+ac-bc$ and $abc$. $$\begin{gathered} rcrab+ac-bc\&\& \\ abc\&\& \\ \mathrm{\backslash hline}{a}^2{b}^{2}c+a^{2}b{c}^2\&-\&a{b}^2{c}^2 \end{gathered}$$

We multiply $ab$, the first term of the multiplicand, by $abc$, and work to the right.

Exercise 21.

Find the product of:

1. $x+7$ and $x$.

2. $2x-3y$ and $4x$.

3. $2x-3y$ and $7y$.

4. $x-2a$ and $2a$.

5. $-x+3b$ and $-b$.

6. $2a^2-3ab$ and $-3a$.

7. $2x^2+3xz$ and $5z$.

8. $a^2-5ab$ and $5ab$.

9. $x^2-3xy$ and $-y^2$.

10. $2x^3-3x^2$ and $2x^2$.

11. $x^2-3y^2$ and $4y$.

12. $x^2-3y^2$ and $-x^2$.

13. $b^3-a^2{b}^2$ and $-a^3$.

14. $-a^2{b}^2-a^3$ and $-a^2$.