math: simplifying algebraic expressions

Where did algebraic Where did algebraic expressions begin?expressions begin?

The history of algebra began in ancient Egypt The history of algebra began in ancient Egypt and Babylon.and Babylon.

The word algebra comes from the Arabic The word algebra comes from the Arabic word "al-jabr", which is in the title of a book by word "al-jabr", which is in the title of a book by mathematician al-Khwarizmimathematician al-Khwarizmi

Simplifying Algebraic Simplifying Algebraic ExpressionsExpressions

Students will represent and Students will represent and evaluate quantities using evaluate quantities using algebraic expressions.algebraic expressions.

VOCABULARYVOCABULARY

Term – a grouping of a number and variablesTerm – a grouping of a number and variables Ex. 7x, 4, 5xyEx. 7x, 4, 5xy

Coefficient – the number multiplied by the Coefficient – the number multiplied by the variablevariable

CoefficientCoefficient VariableVariablex12

Every variable has an Every variable has an understood 1 as its understood 1 as its

coefficient!coefficient!

x = 1xd = 1d

To combine like terms, To combine like terms, you must have the same you must have the same

VARIABLEVARIABLE and and EXPONENTEXPONENT!!

Combining like terms is like Combining like terms is like grouping similar objects.grouping similar objects.

Group Similar VariablesGroup Similar Variables

5x + 7y + 9x + 12z + 2y + 245x + 7y + 9x + 12z + 2y + 24

5x5x + 7y + 7y + 9x + 9x + 12z + 2y + 24+ 12z + 2y + 24

14x14x + 7y + 7y + 12z + 12z + 2y + 2y + 24+ 24

14x14x + 9y + 9y + 12z + 24+ 12z + 24

Example 1Example 1

233 42735 xyxyx

Example 2Example 2

babaa 1454 2

Example 3

22 22 xxx

Example 4Example 4DistributeDistribute

baa 2)2(2 2

Example 5Example 5DistributeDistribute

3(a + 3a + 4b + c – 2a)3(a + 3a + 4b + c – 2a)

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ClassworkClasswork

Complete Complete Page 44Page 44

(2-26) EVEN(2-26) EVEN

Use your colored pencils Use your colored pencils for number 2, 8, and 10.for number 2, 8, and 10.

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