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Combine Like Terms and Distributive Property Combine Like Terms and Distributive Property

Combine Like Terms and Distributive Property - PowerPoint Presentation

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Uploaded On 2015-11-10

Combine Like Terms and Distributive Property - PPT Presentation

Combine Like Terms and Distributive Property In this lesson you will be shown how to combine like terms along with using the distributive property Terms in an algebraic expression are separated by addition or subtraction signs ID: 188986

combine terms distributive property terms combine property distributive coefficients simplify identify coefficient multiply expression means

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Slide1

Combine Like Terms and Distributive PropertySlide2

Combine Like Terms and Distributive Property

In this lesson, you will be shown how to combine like terms along with using the distributive property.Slide3

Terms

in an algebraic expression are separated by addition or subtraction signs.

How many terms are in this expression?

Like terms are terms that look alike.

So, what are like terms?Slide4

More specifically, Like Terms are terms that have the same variable raised to the same power (exponent).

Now, let’s give this a try.Slide5

Combine like terms.

Identify like terms

.

Combine coefficients: 14 – 5 = 9

A.

14

a

– 5

a

9

a

B.

7

y

+ 8 – 3

y

– 1 +

y

Identify like terms ; the coefficient of y is 1, because 1y = y.

5

y

+ 7

Combine coefficients: 7 – 3 + 1 = 5 and 8 – 1 = 7Slide6

Combine like terms.

Identify like terms

; the coefficient of q is 1, because 1q = q.

Combine coefficients: 4 – 1 = 3

Identify like terms;

the coefficient of c is 1, because 1c = c.

6

3

q

C.

4

q

q

D.

5

c

+ 8

– 4

c

– 2 –

c

Combine coefficients: 5 – 4 – 1 = 0 and 8 – 2 = 6Slide7

E. 4

m

+ 9

n

– 2

4m

+ 9n – 2

Combine like terms.

No like terms

.

F. 5

m

*

7

m

– 8 + 4

35

m

– 4 Slide8

Remember, to

simplify

an expression means to perform all possible operations, including combining like terms.

In other words, simplify means solve!Slide9

The Distributive Property

is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.

For any numbers a, b, and c,

a(b + c) =

a(b) + a(c)

and

a(b – c) =

a(b) – a(c)Slide10

Distribute

A. 6(x - 3)

B.

2(y

+ 1)C. 3(a

- 1)

6x - 18

2y + 2

3a – 3Slide11

Now we will use the distributive property first, then combine like terms second.Slide12

1. Simplify 6(5 +

n

)

– 2

n.

Distributive Property

.

Multiply.

6(5 +

n

) – 2n

30 + 6

n

– 2

n

6

(5)

+

6

(

n) – 2n

30 + 4n

Combine coefficients 6

– 2 = 4.Slide13

2. Simplify 3(

c +

7)

c.

Distributive Property

.

Multiply.

3(

c

+ 7) – c

3

c

+ 21

c

3

(

c

)

+ 3(7) –

c2c + 21

Combine coefficients 3

– 1 = 2.Slide14

3. 4(3x + 6)

7x

4. 6(x + 5) + 3x

Simplify.Slide15

4. 5(2x - 3)

+

4x

10x – 15 + 4x

14x - 15