Addition, Subtraction, and Multiplication of Polynomials

Addition, Subtraction, and Multiplication of Polynomials

by JadeAnthony Dosdos

​Addition and Subtraction of Polynomials

​Lesson Objective:

​At the end of the lesson, student should be able to:

​- Add/subtract integers.

​- Add/subtract polynomials.

​Polynomial - may have constants (like 4), variables (x and y) and exponents (like the 2 in the y² , that can be combined using addition, subtraction, multiplication and division.

​Addition of polynomials

​Example: Add 3x³+2x²-x-7 and x³-10x²+8

​

​3x³ + 2x² - x - 7

​ x³ -10x² +8

​4x³ - 8x² - x + 1

​Example: Add 9y³+3y²-2y+1 and -5y²+y-4

​

​9y³ + 3y² - 2y + 1

​ - 5y² + y - 4

​9y³ - 2y² - y - 3

Multiple Choice

Add: 2x³+x²-3x+4 and x³+7x²-2.

• 2x⁶+7x²-3x-2

• 3x²+7x²-5x+2

• 3x³+8x²-3x+2

• 3x³-8x²+5x-2

Multiple Choice

Add: $$3x^2+4x-10$$  + $$3x^3-4x^2+x-12$$  

• $$6x^3+2x^2-3x-2$$  

• $$3x^3-x^2+5x-22$$  

• $$6x^2-x+5x-2$$  

• None of the above

​Subtraction of polynomials:

​Example: 2x³+6x²-x+1 from 8x³-3x²-2x+9.

​

​ 8x³ - 3x² - 2x + 9 8x³ - 3x² - 2x + 9

​- 2x³ + 6x² - x + 1 + -2x³- 6x² + x - 1

​ 6x³- 9x² - x + 8

Multiple Choice

Subtract:  $$3x^3+5x^2-x+8\ from\ -x\ -8$$  .

• $$-3x^3-5x^2-16$$  

• $$3x^2+5x^2-2x+16$$  

• $$3x^2+5x^2-2x-16$$  

• $$-3x^3-5x^2+2x+16$$  

Poll

Do you have any questions?

• YES

• NO

Multiple Choice

Subtract: $$-4x^2+7x+15$$  - $$-7x^2+7x-9$$  

• $$-3x^2-14x+6$$  

• $$-11x^2+14x+6$$  

• $$-11x^2-14x-24$$  

• $$3x^2+24$$  

​Review:

​Direction: Add or subtract in each given:

​1. 3 + (-4) =

​2. (-10) + (-9)=

​3. (-5) - 4 =

​4. 6 - (-3) =

​5. 13 - 20 =

​6. -4 * (-4)=

7. (-3) * 2=

8. (6) * (-5)=​

​Multiplication of Polynomials

​by JadeAnthony Dosdos

​Multiplication examples:

​In your own:

​Special Products

​Core concepts:

​Continued...

​Multiplication of polynomials:

​Example: (2x+7)(2x-7)

​

​Follow the SUM AND DIFFERENCE rule.

​

​a = 2x

​b = 7

​(a+b)(a-b) = a²-b²

​(2x+7)(2x-7) = (2x)² - (7)²

​ =(2)²(x)² - (7)²

​ = 4x² - 49

​Multiply: (6x-2)²

​

​Follow the SQUARE of a BINOMIAL (since the exponent is 2 and the operation is minus).

​

​a = 6x

​b = 2

​

​​(a-b)²= a² - 2ab + b²

​ = (6x)² - 2(6x)(2) + (2)²

​ = (6)² (x)² - 12x(2) + 4

​ = 36x² - 24x + 4

​Multiply: (x+4)³

​

​Follow the CUBE of a BINOMIAL (since the exponent is 3 and the operation is addition).

​

​a = x

​b = 4

​(a+b)³ = a³ + 3a²b + 3ab² + b³

​ = x³ + 3(x)² (4) + 3(x)(4)² + (4)³

​ = x³ + 12x² + 3(x)(16) + 64

​ = x³ + 12x² + 48x + 64

Multiple Choice

Multiply: (3x+2)²

• -6x² - 5x + 4

• -9x² - 12x - 4

• 6x² + 5x + 4

• 9x² + 12x + 4

Multiple Choice

Multiply: (x-1)³

• x³ + 3x - 1

• x³ - 3x² + 3x - 1

• -x³ + 3x - 1

• x³ + 3x² + 3x + 1