# Algebra - Mixed Practice (Up to Polynomial Manipulation)

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## Algebra - Mixed Practice (Up to Polynomial Manipulation)

In this set of worksheets, we cover material from pre-algebra up to manipulation of polynomials (adding, subtracting, and multiplying).

Also included is practice with fractions, positives and negatives, nested parentheses, writing expressions, and solving equations.

Scroll down for a listing of all worksheet sets in this series.

**Worksheet 4.1**

- Positives and Negatives, with variables
- Fraction manipulation, with variables
- Writing expressions
- Adding and subtracting polynomials

**Worksheet 4.2**

- Simplifying expressions with nested parentheses
- Solving equations
- Adding and subtracting polynomials (including fractional coefficients)
- Multiplying polynomials

## Worksheet Sets in this Series

Worksheets for this section are below the index. Click the "Overview" link to get a more detailed view of the entire series.

**Mixed Practice Overview**- Mixed Practice #1 - Pre-Algebra
- Mixed Practice #2 - Algebraic Expressions
- Mixed Practice #3 - Linear Equations
- Mixed Practice #4 - Polynomial Manipulation
- Mixed Practice #5 - Factoring
- Mixed Practice #6 - Quadratic Equations
- Mixed Practice #7 - Rational Expressions
- Mixed Practice #8 - Systems of Equations
- Mixed Practice #9 - Radical Expressions

Lesson by Mr. Twitchell

## Handouts/Worksheets

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## Mixed Practice 4.1

- 3x + (-2x) - (5x) - (-2x) =

- -2y - 3y + (-y) - (-4y) =

- 5z + (-3z) - (2z) =

- 11w - (-10w) + (-12w) =

- x +13x =52

- y -34y =12

- -z -25z =35

- w - (-17w) =15
*Write an expression and simplify*

- Seven less than a number

- The sum of a number and that number decreased by three

- The difference between a number and two less than that number

- Five less than a number, increased by four more than that number

- Twice the cost of three apples and two oranges
*Perform the operation; write your answer in descending order*

- Add 5x + 2x
^{2}+ 3 and 5x^{2}- 2x + 5

- Add -3y - 7 + 2y
^{2}and -4y^{2}+ 1

- Add 1 + 12y
^{3}and 5y^{2}- 2y

- Subtract 3x + 10 from 5x
^{5}- 2x + 20

- Subtract x
^{2}- x + 1 from x^{2}+ x - 1

- Subtract -3x - 5x
^{2}from 10x + 1

- Subtract 2x
^{2}+ 1 from 3x^{2}+ 3x + 3

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## Mixed Practice 4.1: Answer Key

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## Mixed Practice 4.2

- 3x - 2[x - 5(1 + x)] =

- 10 + (-3)[x - 4(x + (-1))] + 2x =

- 12x + 3(5 - y) + 2[2x + 3y - (x + y)] =

- 2(x + y) - 2(x - y) + 4(y - x) =
*Solve the equations*

- 3x + 2 = 20

- 2x - 7 = x + 24

- 2(x + 1) = 3(x - 10)

- 2 - (x - 2) = 20

- (x - 12) = 1513

- 3[x + 2(x - 5)] = 87
*Perform the operation; write your answer in descending order*

- Add + 3x and 7 - 2x103
^{2}

- Add 1 + x - x12
^{2}and 2 -x + x23^{2}

- Subtract x + 1 from x
^{3}+ x + x^{2}+ 1

- Subtract -110x from15x13
^{2}++25x110

- (x + 1)(x - 1) =

- (2x + 1)(x
^{2}+ x) =

- (x + 1)(x
^{2}- x + 1) =

- (5x - 7)
^{2}=

- (x + 1)(x + 1)(x + 1) =

- (x - 2)(x - 2)(x - 2) =

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## Mixed Practice 4.2: Answer Key

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