2. 1.Multiply a polynomial by a monomial. 2.Multiply a polynomial by a polynomial.

3. The Distributive Property Look at the following expression: 3(x + 7) This expression is the sum of x and 7 multiplied by 3. To simplify this expression we can distribute the multiplication by 3 to each number in the sum. (3 x)+(3 7) 3x + 21

4. Multiply: 3xy(2x + y) This problem is just like the review problems except for a few more variables. To multiply we need to distribute the 3xy over the addition. 3xy(2x + y) =(3xy 2x) + (3xy y) = Then use the order of operations and the properties of exponents to simplify. 6x 2 y + 3xy 2

5. It is also advantageous to multiply polynomials without rewriting them in a vertical format. Multiply: (x + 2)(x – 5) Though the format does not change, we must still distribute each term of one polynomial to each term of the other polynomial. Each term in (x+2) is distributed to each term in (x – 5).

6. (x + 2)(x – 5) This pattern for multiplying polynomials is called FOIL. Multiply the First terms. Multiply the Outside terms. Multiply the Inside terms. Multiply the Last terms. F O I L After you multiply, collect like terms.

7. Example: (x – 6)(2x + 1) x(2x)+ x(1)– (6)2x– 6(1) 2x 2 + x – 12x – 6 2x 2 – 11x – 6

8. Another Example Multiply (x – 2) 2 This means (x – 2)(x – 2) Do the Foil Method FOILFOIL Combine like terms (if any) x 2 – 4x + 4 x 2 -2x-2x4

9. 1. 2x 2 (3xy + 7x – 2y) 2. (x + 4)(x – 3) 3. (2y – 3x)(y – 2)

10. 2x 2 (3xy + 7x – 2y) 2x 2 (3xy) + 2x 2 (7x) + 2x 2 (–2y) 2x 2 (3xy + 7x – 2y) 6x 3 y + 14x 2 – 4x 2 y

11. (x + 4)(x – 3) (x + 4)(x – 3) x(x) + x(–3) + 4(x) + 4(–3) x2 x2 – 3x + 4x – 12 x2 x2 + x –

12. (2y – 3x)(y – 2) (2y – 3x)(y – 2) 2y(y) + 2y(–2) + (–3x)(y) + (–3x)(–2) 2y 2 – 4y – 3xy + 6x