5.3 Addition and Subtraction of Polynomials

​Addition and Subtraction of Polynomials

​

多項式的加減法​

​We have learned...

• Monomials 單項式

• Polynomials​ 多項式

​Like terms and Unlike terms

同類項 和 異類項​

• ​Like terms 同類項：

  Two or more terms having the same variables to the same indices.

  兩個或以上的項中，變數相同、且各變數的指數也相同。

​

​

​Examples of Like terms: 同類項的例子

2a and 4a​ 5xy and 7xy

3x and -5x​ 6a²b and 7a²b

3ab and 4ab​ 6a²b⁴ and 7a²b⁴

• ​Unlike terms 異類項

  Terms that are not like terms.

  不是同類項的項就叫異類項。

​Like terms and Unlike terms

同類項 和 異類項​

​Examples of Unlike terms: 異類項的例子

3x and 4y

3x²y and 5xy​²

Multiple Select

Choose all the like terms

• 3x

• -5x

• 7xy

• 6x

Multiple Choice

Determine whether -10m and -10 is like terms or not

• Yes, they are like terms.

• No, they are unlike terms.

Draw

Write down a like terms of 2ab and -ab:

​Combing Like terms 合併同類項

​For example,

​3a+5a = (3+5)a = 8a

​

5m-2m = (5-2)m = 3m​

​You cannot combine Unlike terms

異類項則不可合併​

​For example,

2m²+m²+3​ = (2+1)m²+3 =3m²+3

​

4xy-2x-5x​ = 4xy-(2+5)x = 4xy-7x

Draw

Simplify 5x³+4x³

Draw

Simplify 4xy-9xy

Draw

Simplify 4a+8a-3

​Adding and Subtracting Polynomials

多項式的相加和相減​

​Steps:

1. Removing brackets 拆括號

2. Grouping like terms 把同類項放在一起

3. Combing like terms​ 合併同類項

Draw

Remove the brackets: +(-3x)

Draw

Remove the brackets: -(+6y)

Draw

Remove the brackets: +(2a)

Draw

Remove the brackets: -(-9b)

Draw

Remove the brackets: +(2a-3b)

Draw

Remove the brackets: +(-6x+4y)

Draw

Remove the brackets: -(7u-4v)

Draw

Remove the brackets: -(-2p-q)

​Summary of today's lesson,

We learned...

• ​Like terms

• Unlike terms

• Combining like terms

• Removing the brackets

• Simplify (Adding or Subtracting) Polynomials​

Poll

Vote: Today, I learned...

• I can determine like terms and unlike terms after this lesson.

• I know how to remove brackets after this lesson.

• I know how to combine like terms after this lesson.

• I can calculate addition and subtraction of polynomials after this lesson.