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