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Chapter Contents

• Basic Algebra
• 1. Addition and Subtraction of Algebraic Expressions
• 2. Multiplication of Algebraic Expressions
• 3. Division of Algebraic Expressions
• 4. Solving Equations
• 5. Formulas and Literal Equations
• 6. Applied Verbal Problems
• Algebra Problem Solver

• Comments, Questions?

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2. Multiplication of Algebraic Expressions

When we multiply algebraic expressions, we need to remember the Index Laws from the Numbers chapter.

Let's see how algebra multiplication works with a series of examples.

Example 1

Multiply x³(x⁴ + 5a)

Answer

Example 2

Multiply (x + 5)(a − 6)

Answer

Example 3

Multiply (2x + 3)(x² − x − 5)

Answer

Example 4

Multiply (x − 3)²

Answer

Here is a LiveMath document to illustrate this. You can make changes like changing x to some other letter, change the minus to plus, etc. Observe what happens at each change.

LIVEMath

Important Note:

(x − 3)²

is NOT equal to

x² − 9

Example 5

Simplify 5x[- 4 + 10(x - y)] + 7x

Answer

 

Example 6

An expression found in chemical thermodynamics is p(c − 1) + 2 − c(p − 1). Multiply and simplify.

Answer