Add, Subtract and Multiply Polynomials

Add, Subtract, Multiply Polynomials

Steps to adding Polynomials

• 1. Remove Parenthesis

• 2. Identify like terms (notice that he makes boxes around x³, circles around x, and underlines the constants (number only)

• 3. Add like terms [boxes with boxes] (circles with circles), underline w/ underline

• 4. Write in standard form (highest exponent to lowest)

Be sure to write each problem down so that you can work it out on your own.

You can only combine terms that have the same variable and same exponential degree

Multiple Choice

Which of the following are examples of like terms?

• 2 and 2x
• y³ and x³
• y and x
• -3x and 3x

Multiple Choice

Find the sum. (3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

• 3y³ + 7y² - 4y + 3

• 4y² + 3y³ - y + 3

• -y⁴ + 2y³ -y - 4

• 4y³ + 3y² -3y + 1

Multiple Choice

Simplify (9x + 17) + (19x - 27)

• 28x + 44

• 28x - 10

• -28x + 10

• -171x - 459

Multiple Choice

Simplify (-8v⁴ + 4v³ + 3v) + (- 8v⁴ + 4v - 7)

• -17v⁴ + 4v³ + 2v - 7

• -16v⁴ + 4v³ + 10v - 7

• -16v⁴ + 4v³ + 7v - 7

• -16v⁴ + 4v³ + 2v - 7

Multiple Choice

Find the sum (2x² + 5x - 7) + ( 3 - 4x² + 6x)

• 2x² + 3x +1

• -2x² - 11x -4

• 2x²+ 5x -7

• -2x² + 11x -4

Multiple Choice

Add the polynomials.
(2x + 5y) + (3x - 2y)

• 3x + 5y
• 5x + 3y
• 5x + 7y
• 7xy + 1xy

Steps to subtracting Polynomials

• 1. Distribute negative (changes the sign in front of each term)

• 2. Identify like terms (notice that he makes boxes around x³, circles around x, and underlines the constants (number only)

• 3. Add like terms [boxes with boxes] (circles with circles), underline w/ underline

• 4. Write in standard form (highest exponent to lowest)

Be sure to write each problem down so that you can work it out on your own.

You can only combine terms that have the same variable and same exponential degree

Multiple Choice

One difference between adding and subtracting polynomials is...

• Using the associative property

• Using the distributive property

• Using the commutative property

• Nothing. The process is the same

Multiple Choice

Add or Subtract to Simplify:
(4x²+ x) - (x²+ 2x)

• 3x² - x
• 4x² + 2x
• 3x² + 3x
• 3x² + 2x

Multiple Choice

Simplify:

• 9n³ + 4n
• 7n³ + 6
• -3n³ + 2
• 7n⁶ + 6

Multiple Choice

(x³-x²+4) - (3x³-2x²+3)

• -2x³-3x²+7
• -2x³+x²+1
• 2x³-3x³-1
• 4x³-3x²+7

Multiple Choice

Simplify each expression.

(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

• -8n² - 8n + 3

• -7n² - 8n + 3

• -6n² - 8n + 3

• -7n² - 4n + 3

Multiple Choice

Add or Subtract to Simplify:
(5x + x² - 4) - (4x - x² + 6)

• 2x² + x + 2 
• x + 2
• 2x² + x - 10 
• x - 10 

Multiply Poly Steps

• 1. Set up a grid-like system so that each term has its own box (be sure to include the sign in front of the term!)

• 2. Multiply each term. Multiply the coefficients (number in-front) & add the exponents

• 3. Combine like terms & Write in standard form

Be sure to write each problem down so that you can work it out on your own.

You can only combine terms that have the same variable and same exponential degree

Multiple Choice

Which box is correctly solved for (8x+3)(7x-1)

Multiple Choice

Which of the following is the correct box method set-up to solve $$\left(x+2\right)\left(x+3\right)=$$  ?

Multiple Choice

Write the expanded (general) form of the product (x+3)(x+6).

• x²+18x+9

• x²+9x+18

• x²+18x+18

Multiple Choice

(3a) Select the answer that completes the box with the correct terms. The terms are listed in 1, 2, 3, 4 order as shown in the box.

• $$-4x^3,\ 8x^2,\ -2x,\ 4$$

• $$-4x^2,\ 8x^2-2x,\ 4x$$

• $$4x^3,\ -8x^2,\ 2x,\ -4$$

• $$4x^2,\ -8x^2,\ -2x\ ,\ -4x\$$

Multiple Choice

(4p − 1)(4p - 1)

• 16p² + 1
• 16p² − 1
• 16p² − 8p + 1
• 16p² + 8p + 1

Multiple Choice

Simplify: 
$$\left(x+7\right)\left(x-7\right)$$  

• $$x^2+7x-49$$  

• $$x^2-7x+49$$

• $$x^2-49$$

• $$x^2+49$$  

Multiple Choice

(x-3)(x²+2x+7)

• x³-x²+x-21
• x³+5x+13x-21
• x³-3x²+7x-21
• x²+2x-3