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Simplifying Expressions
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Hint: The idea is that the variable part of the terms must be identical for them to be like terms.

Slide 11

Examples

Examples

Like Terms

5x , -14x

-6.7xy , 02xy

The variable factors are

identical.

Unlike Terms

5x , 8y

The variable factors are

not identical.

Slide 12

Combining Like Terms

Combining Like Terms

Recall the Distributive Property

a (b + c) = b(a) +c(a)

To see how like terms are combined use the

Distributive Property in reverse.

5x + 7x = x (5 + 7)

= x (12)

= 12x

Slide 13

Example

Example

All that work is not necessary every time.

Simply identify the like terms and add their

coefficients.

4x + 7y x + 5y = 4x x + 7y +5y

= 3x + 12y

Slide 14

Collecting Like Terms Example

Collecting Like Terms Example

Slide 15

Both Skills

Both Skills

This example requires both the Distributive

Property and combining like terms.

5(x 2) 3(2x 7)

Distribute the 5 and the 3.

x(5) - 2(5) + 2x(-3) - 7(-3)

5x 10 6x + 21

Combine like terms.

- x+11

Slide 16

Simplifying Example

Simplifying Example

Slide 17

Simplifying Example

Simplifying Example

Distribute.

Slide 18

Simplifying Example

Simplifying Example

Distribute.

Slide 19

Simplifying Example

Simplifying Example

Distribute.

Combine like terms.

Slide 20

Simplifying Example

Simplifying Example

Distribute.

Combine like terms.

Slide 21

Evaluating Expressions

Evaluating Expressions

Remember to use correct order of operations.

Evaluate the expression 2x 3xy +4y when

x = 3 and y = -5.

To find the numerical value of the expression, simply replace the variables in the expression with the appropriate number.

Slide 22

Example

Example

Evaluate 2x3xy +4y when x = 3 and y = -5.

Substitute in the numbers.

2(3) 3(3)(-5) + 4(-5)

Use correct order of operations.

6 + 45 20

51 20

31

Slide 23

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