multiplying polynomials
4.5 Multiplying Polynomials
In this case, both polynomials have two terms. You need to distribute both terms of one polynomial times both terms of the other polynomial.
One way to keep track of your distributive property is to
Use the FOIL method. Note that this method only works on (Binomial)(Binomial). F First terms
O Outside terms
I Inside terms
L Last terms As mentioned above, use the distributive property until every term of one polynomial is multiplied times every term of the other polynomial. Make sure that you simplify your answer by combining any like terms.
Example Multiply .
*Use Dist. Prop. twice
*Combine like terms
4.1 Product Rule and Power Rule for Exponents
Multiplying with same base – add exponents
Example 1: (2x) (3x) = (2)(3)x1+1 = 6x² Example 2: (2x³) (3x²) = (2)(3)x3+2 = 6x5
Power Raised to a Power – multiply exponents
Example 1: (2x3)3 = 23x3•3 = 8x9 Example 2: 2(x3)-2 = 2x-6 = 2 X6
Example 3: 2(x3)4 = 2x3•4 = 2x12
Remember, the “2” and the exponent of 4 have nothing to do with each other because the 2 is not inside the parenthesis.
2.5 Geometry Formulas
Solving a literal equation follows the same rules as solving a linear equation. A literal equation differs from other equations because you are not solving for a specific value for a specific variable.
i. Solve for b. This is the formula for the area of a triangle.
As with the problem shown earlier, this equation is solved for A. To solve for b, you should start by multiplying both sides by 2 to get rid of the fraction. Now to have b by itself, divide by sides by h. ii. Solve for h. This is the formula for the volume of a cylinder.
To solve for h, you will need to divide both sides by and .
In this case, both polynomials have two terms. You need to distribute both terms of one polynomial times both terms of the other polynomial.
One way to keep track of your distributive property is to
Use the FOIL method. Note that this method only works on (Binomial)(Binomial). F First terms
O Outside terms
I Inside terms
L Last terms As mentioned above, use the distributive property until every term of one polynomial is multiplied times every term of the other polynomial. Make sure that you simplify your answer by combining any like terms.
Example Multiply .
*Use Dist. Prop. twice
*Combine like terms
4.1 Product Rule and Power Rule for Exponents
Multiplying with same base – add exponents
Example 1: (2x) (3x) = (2)(3)x1+1 = 6x² Example 2: (2x³) (3x²) = (2)(3)x3+2 = 6x5
Power Raised to a Power – multiply exponents
Example 1: (2x3)3 = 23x3•3 = 8x9 Example 2: 2(x3)-2 = 2x-6 = 2 X6
Example 3: 2(x3)4 = 2x3•4 = 2x12
Remember, the “2” and the exponent of 4 have nothing to do with each other because the 2 is not inside the parenthesis.
2.5 Geometry Formulas
Solving a literal equation follows the same rules as solving a linear equation. A literal equation differs from other equations because you are not solving for a specific value for a specific variable.
i. Solve for b. This is the formula for the area of a triangle.
As with the problem shown earlier, this equation is solved for A. To solve for b, you should start by multiplying both sides by 2 to get rid of the fraction. Now to have b by itself, divide by sides by h. ii. Solve for h. This is the formula for the volume of a cylinder.
To solve for h, you will need to divide both sides by and .