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Warm Up Add. 1. 427 + 35. 1.80. 2. 1.06 + 0.74. 462. 3. 10. Multiply. 4. 25(8). 5. 1.3(22). 28.6. 200. 6. The Distributive Property is used with Addition to Simplify Expressions.

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Presentation Transcript
slide1

Warm Up

Add.

1. 427 + 35

1.80

2. 1.06 + 0.74

462

3.

10

Multiply.

4. 25(8)

5. 1.3(22)

28.6

200

6.

slide2

The Distributive Property is used with Addition to Simplify Expressions.

The Distributive Property also works with subtraction because subtraction is the same as adding the opposite.

slide3

The terms of an expression are the parts to be added or subtracted. Like terms are terms that contain the same variables raised to the same powers. Constants are also like terms.

Like terms

Constant

4x –3x + 2

slide4

A coefficientis a number multiplied by a variable. Like terms can have different coefficients. A variable written without a coefficient has a coefficient of 1.

Coefficients

1x2 + 3x

slide5

Using the Distributive Property can help you combine like terms. You can factor out the common factors to simplify the expression.

7x2 – 4x2 = (7 – 4)x2

Factor out x2 from both terms.

= (3)x2

Perform operations in parenthesis.

= 3x2

Notice that you can combine like terms by adding or subtracting the coefficients and keeping the variables and exponents the same.

slide6

Example 3A: Combining Like Terms

Simplify the expression by combining like terms.

72p – 25p

72p –25p

72p and 25p are like terms.

47p

Subtract the coefficients.

slide7

and are like terms.

Write 1 as .

Example 3B: Combining Like Terms

Simplify the expression by combining like terms.

A variable without a coefficient has a coefficient of 1.

Add the coefficients.

slide8

Example 3C: Combining Like Terms

Simplify the expression by combining like terms.

0.5m + 2.5n

0.5m + 2.5n

0.5m and 2.5n are not like terms.

0.5m + 2.5n

Do not combine the terms.

slide9

3m2 + m3

Check It Out! Example 3

Simplify by combining like terms.

3a. 16p + 84p

16p + 84p

16p + 84p are like terms.

100p

Add the coefficients.

3b. –20t – 8.5t2

–20t – 8.5t2

20t and 8.5t2 are not like terms.

–20t – 8.5t2

Do not combine the terms.

3c. 3m2 + m3

3m2 + m3

3m2 and m3are not like terms.

Do not combine the terms.

slide10

Example 4: Simplifying Algebraic Expressions

Simplify 14x + 4(2 + x). Justify each step.

Procedure

Justification

1.

14x + 4(2 + x)

2.

14x + 4(2) + 4(x)

Distributive Property

3.

14x + 8 + 4x

Multiply.

Commutative Property

4.

14x + 4x + 8

5.

(14x + 4x) + 8

Associative Property

6.

18x + 8

Combine like terms.

slide11

Check It Out! Example 4a

Simplify 6(x –4) + 9.Justify each step.

Procedure

Justification

1.

6(x –4) + 9

2.

Distributive Property

6(x)–6(4) + 9

3.

6x – 24 + 9

Multiply.

Combine like terms.

4.

6x – 15

slide12

Check It Out! Example 4b

Simplify −12x – 5x + 3a + x.Justify each step.

Procedure

Justification

1.

–12x – 5x + 3a + x

2.

Commutative Property

–12x – 5x + x + 3a

3.

–16x + 3a

Combine like terms.

slide13

Lesson Quiz: Part II

Simplify each expression by combining like terms. Justify each step with an operation or property.

5.

14c2 – 9c

6. 14c2 – 9c

7. 301x – x

300x

8. 24a + b2 + 3a + 2b2

27a + 3b2