Multiplying Polynomials (Box and Distributive Methods)

Multiplying Polynomials (Box and Distributive Methods)

Multiply Polynomials

• When multiplying polynomials, remember the rules of exponents

• 1. when multiplying same bases, add exponents

• 2. when dividing same bases, subtract exponents

• 3. when raising a power to a power, multiply exponents

• 4. any number to the zero power is 1

Multiplying Polynomials by the Box Method

• 1. Create a box divided into columns and rows equal to the number of terms in each polynomial

• 2. Write one polynomial across the top of the box, with each term corresponding to a cell. Put the sign of the term in the cell with the polynomial.

• 3. Write the other polynomial down the side of the box, with each term corresponding to a cell.

• 4. Put the sign of the term next to the term, not above

Multiplying Polynomials by the Box Method

• 5. Multiply the upper polynomial by the first term of the side polynomial and write it in the cell underneath the term

• 6. Multiply the upper polynomial by the second term of the side polynomial and write it in the cell underneath the term

• 7. Continue until you have multiplied the top polynomial by every term in the side polynomial

• 8. Simplifying by adding like terms.

• Notice the like terms follow a diagonal line

Multiplying Polynomials: Rainbow or Distributive Method

• 1. Called the rainbow method because of the lines of distribution

• 2. Multiply everything in the second polynomial by the first term in the first polynomial (along with the sign)

• 3. Multiply everything in the second polynomial by the second term (along with the sign)

Multiplying Polynomials: Rainbow or Distributive Method

• 4. Continue the process until there are no more terms in the first polynomial to multiply by

• 5. Simplify by combining like terms.

Multiple Choice

(5x+2)(x²-3x+6)

• 5x³ - 17x² +24x +12

• 5x³ + 17x² - 24x +12

• 5x³ - 13x² + 24x +12

• 5x³ +13x² - 24x - 12

Multiple Choice

Simplify:

2x ( -2x -3)

• -4x - 3

• x² - 3

• -4x² - 6x

• -4x - 6

Multiple Choice

(5x+2)(x²-3x+6)

• 5x³ - 17x² +24x +12

• 5x³ + 17x² - 24x +12

• 5x³ - 13x² + 24x +12

• 5x³ +13x² - 24x - 12

Multiple Choice

(x - 7)(x + 7)

• x² + 7x - 49

• x² - 7x + 49

• x² - 49

• x² + 49

Multiple Choice

(x + 12)(x - 12)

• x² - 144

• x² + 144

• x² + 12x - 144

• x² - 12x + 144

Multiple Choice

(x - 3)(x +10)

• x² - 7x + 13

• x² - 6x - 30

• x² + 7x - 30

• x² + 13x + 30

Multiple Choice

(x + 7)(x + 9)

• x² + 63x + 16

• x² + 16x + 63

• x² + 79

• x² + 16x + 2