exponent

subtract

multiply

Pre-Algebra

Essential Question: How do we perform multiple operations with polynomials?

Lesson Summary

When working with multiple operations, always follow PEMDAS!

Simplify the expression below.

4(4x – 5) + 2(3x2 + 5x – 1) 4(4x – 5) + 2(3x2 + 5x – 1)

16x – 20 + 6x2 + 10x – 2 16x – 20 + 6x2 + 10x – 2

6x2 + 26x – 22 Simplify the expression below.

(x – 2)2 – (x + 6)(x + 5)

(x – 2)2 – (x + 6)(x + 5) (x – 2)(x – 2) – (x + 6)(x + 5)

x2 – 2x – 2x + 4 x2 + 5x + 6x + 30 x2 – 4x + 4 x2 + 11x + 30

(x2 – 4x + 4) – (x2 + 11x + 30) (x2 – 4x + 4) – 1(x2 + 11x + 30) x2 – 4x + 4 – x2 – 11x – 30

x2 – 4x + 4 – x2 – 11x – 30

-15x – 26

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

Multiply first: distribute 4 and 2 to each term in ( )

Result after distributing the 4 and 2.

Combine like terms.

Final Answer

Parentheses

Exponents

Multiplication

or

Division

Addition

or

Subtraction

Steps to Simplifying:

1) Raise (x – 2) to the second power and multiply (x + 6) and (x + 5) first. Multiplication comes before subtraction.

2) Place the products in parentheses before subtracting.

3) In order to subtract the products, distribute

the – sign or a -1.

4) Combine like terms.

5) Represent final answer in standard form.

Examples

Simplify each expression. All answers should be written in standard form.

1. (3x)(-4x) – (5x2 – 3x + 1) 2. (9x2 – 3x + 2) – (x + 4)2

3. What is the result when the sum of 2x2 + 4x + 3 and -6x – 1 is multiplied by – 2

1x3 ?

SCROLL DOWN FOR THE PRACTICE PROBLEM SET

-12x2 – 1(5x2 – 3x + 1)

-12x2 – 5x2 + 3x – 1

-17x2 + 3x – 1

1) Multiply 3x and -4x 2) Subtract by distributing the – sign or -1 3) Combine like terms 4) Write final answer in standard form.

(9x2 – 3x + 2) – (x + 4)(x + 4) (9x2 – 3x + 2) – [(x + 4)(x + 4)] (9x2 – 3x + 2) – (x2 + 4x + 4x + 16) (9x2 – 3x + 2) –1(x2 + 8x + 16)

9x2 – 3x + 2 – x2 – 8x – 16

8x2 – 11x – 14

1) Rewrite (x + 4)2 as (x + 4)(x + 4) 2) Multiply x + 4 by x + 4 and keep the product in ( ) 3) Subtract the result from 9x2 – 3x + 2 4) Subtract by distributing the – sign or -1 5) Combine like terms

1st: Find the sum of 2x2 + 4x + 3 and -6x – 1 first.

(2x2 + 4x + 3) + (-6x – 1) 2x2 + 4x + 3 – 6x – 1 Combine like terms 2x2 – 2x + 2

2nd: Multiply the sum (2x2 – 2x + 2) by – 2

1x3

– 2

1x3(2x2 – 2x1 + 2) Distribute the monomial –

x3 to each term in the ( )

-1x5 + 1x4 – 1x3 Multiply coefficients and add variable exponents

-x5 + x4 – x3

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.

Simplify each expression. All answers should be written in standard form.

1. 4(2x – 6)2 2. -5(x – 2) + 7x(x2 – 9x + 1)

3. (4x – 5)(4x + 5) – (2x – 10)(2x + 10)

4. If the difference of 3x – 5 and 7x2 – 5x + 4 is multiplied by 2x2, what is the result?