Multiplying Simple Polynomials

Multiplying Polynomials (All 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

• When multiplying polynomials, you will be using the distributive property

• Remember how the distributive property works: when an expression is being multiplying by a term, distribute, or multiply, every term in the expression by the term

• (3)(5x + 5) = 3 (5x) + 3(5)

Multiplying Polynomials by the Box Method

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

• 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.

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

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

Multiplying Polynomials by the Box Method

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

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

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

• 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.

Multiplying Polynomials by the F.O.I.L. Method

• F.O.I.L. stands for First Outside Inside and Last.

• It is not the same as rainbow. You do not distribute the terms in the first polynomial.

• Multiply FIRST terms; Multiply OUTSIDE terms; Multiply INSIDE terms; Multiply LAST termss.

Multiplying Polynomials by the Vertical Method

• Similar to multiplying whole numbers

• Similar to distributive property in a vertical method

• Multiply the top number by each term in the bottom number, starting from the right of the bottom number

• Stack like terms under each other as you multiply

• Combine and simplify

Multiplying Polynomials

Each method of multiplying polynomials produces the same results.

Remember to use the rules of exponents when multiplying the variable terms

Multiple Choice

(3x − 6)(7x + 7)

• 21x² − 63x + 42

• 21x² − 21x − 42

• 21x² − 42

• 21x² + 63x + 42

Multiple Choice

(3x − 6)(7x + 7)

• 21x² − 63x + 42

• 21x² − 21x − 42

• 21x² − 42

• 21x² + 63x + 42

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

(4x+1)(5x−2)

• 20x² + 3x − 2

• 20x² − 11x + 5

• 20x² − 18x + 2

• 20x² − 3x − 2

Multiple Choice

(2x - 1)(x + 2)

• 2x² + 3x - 2

• 2x² - 5x - 2

• 2x² + 3x + 2

• 2x² - 5x + 2

Multiple Choice

Multiply 7x²y³ (2x⁴y⁵+6xy³)

• 14x⁸y¹⁵+42x²y⁹

• 9x⁶y⁸+13x³y⁶

• 14x⁶y⁸+42x³y⁶

• 14x⁶y⁸+42x²y⁶

Multiple Choice

Simplify:

2x ( -2x -3)

• -4x - 3

• x² - 3

• -4x² - 6x

• -4x - 6

Multiple Choice

Simplify:

2x ( -2x -3)

• -4x - 3

• x² - 3

• -4x² - 6x

• -4x - 6