Pre-Algebra

Essential Question: How do we add and subtract polynomials?

Lesson Summary

Adding Polynomials 1) Combine like terms (like terms have the same variable raised to the same power) 2) When combining like terms, only add coefficients (keep the variable and exponent the same) Example: Find the sum of 2x2 + 7x – 1 and 9x2 – 5x.

Trinomial Binomial

(2x2 + 7x – 1) + (9x2 – 5x)

2x2 + 7x – 1 + 9x2 – 5x

2x2 + 7x – 1 + 9x2 – 5x

11x2 + 2x – 1

Subtracting Polynomials 1) Distribute the – sign to each term inside the parentheses ( ) which follows the – sign 2) Combine like terms (like terms have the same variable raised to the same power) 3) When combining like terms, only add coefficients (keep the variable and exponent the same) Example: Find the difference of 6x2 + 4x – 2 and 3x2 – 2x + 7. Trinomial Trinomial

(6x2 + 4x – 2) – (3x2 – 2x + 7)

(6x2 + 4x – 2) –1(3x2 – 2x + 7)

6x2 + 4x – 2 – 3x2 + 2x – 7

6x2 + 4x – 2 – 3x2 + 2x – 7

3x2 + 6x – 9

Before reviewing the lesson and completing the practice problem set, watch the VIDEO!

Rewrite expression with parentheses ( )

Rewrite without parentheses ( )

Combine like terms

Write your final answer in standard form

Rewrite expression with parentheses ( )

Distribute the – sign by multiplying each term in ( ) by -1

Rewrite without parentheses ( )

Combine like terms

Write your final answer in standard form

2x2 – 4

x2 – 3x + 8

Examples

Perform the indicated operation. Write all answers in standard form.

1. 3r2 – 6 + 7r + 5r2 – r 2. (6x2 + 4) + (-5x3 + 2x2 – 2) 3. (y3 + 4y – 8) – (9y2 + 2y) 4. (8x4 + 3) + (2x3 – 6x2 + 4) – (-5x4 – 7x2) (y3 + 4y – 8) –1(9y2 + 2y) (8x4 + 3) + (2x3 – 6x2 + 4) –1(-5x4 – 7x2)

5. Subtract 4a2 – 1 from 7a2 + 3a – 2 .

Practice Problem Set

ATTENTION ALL PRE-ALGEBRA STUENTS: We want to remind you that you and your peers create a learning community. We encourage you to face time, text or use any other appropriate communication to reach out to a friend and discuss your answers to the following questions. Working together and having meaningful mathematical discussions aids in your understanding of the subject matter.

Perform the indicated operation. Write all answers in standard form.

1. (5p2 – 3) + (2p2 – 3p) 2. (-4k3 + 14 + 3k2) + (-3k3 – 14k2 – 8)

3. (3 – 6n2 – 8n) – (-6n2 + 3n – 1) 4. Subtract 10x3 – 2x from 8x3 – x + 6

5. Represent the perimeter of the rectangle as a simplified polynomial expression in standard form. Hint: To find the perimeter of any shape, sum all the sides.

3r2 – 6 + 7r + 5r2 – 1r

8r2 + 6r – 6

6x2 + 4 – 5x3 + 2x2 – 2

6x2 + 4 – 5x3 + 2x2 – 2

-5x3 + 8x2 + 2

y3 + 4y – 8 – 9y2 – 2y

y3 + 4y – 8 – 9y2 – 2y

y3 – 9y2 + 2y – 8

8x4 + 3 + 2x3 – 6x2 + 4 + 5x4 + 7x2

8x4 + 3 + 2x3 – 6x2 + 4 + 5x4 + 7x2

13x4 + 2x3 + x2 + 7

(7a2 + 3a – 2) – (4a2 – 1) From comes first! Put ( ) around each polynomial expression. (7a2 + 3a – 2) –1(4a2 – 1) Distribute the – sign by multiplying each term by -1.

7a2 + 3a – 2 – 4a2 + 1

7a2 + 3a – 2 – 4a2 + 1

3a2 + 3a – 1