Simplify and Identify Like Terms in Expressions
4) Which expression is represented by the bar model?
4) Which expression is represented by the bar model?
variable
coefficient
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Simplify
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5a
5a
And another…
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Collecting ‘like’ terms
Algebraic expressions can be simplified by
collecting like terms
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(and their powers such as the 2 in x
2
) are the
same.
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Simplify
5d
4d
d
5d
d
-d
And another…
2e
2
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2
3e
2
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2
+ 2e
2
3e
2
And another…
3b
b
6a + 4b
2a
4a
2a
4a
3b
b
3b
b
2a
4a
6a + 4b
And another…
-3b
b
2a – 2b
-2a
4a
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Simplify the following
expressions by collecting like
terms.
4d + d + 3d
8d
5d -2d + 3d
6d
5p + 4q – 2p + q
3p + 5q
5s - t +s + t
6s
2p
2
+3p
2
– 4p
2
p
2
3pq - 4 + 5pq
8pq - 4
Worked Example
Your Turn
3p
2p
In your books, fully simplify each expression
Mark your work
Algebra Pyramids
In this set of math exercises, you will learn to simplify expressions by combining like terms. You will also identify the variable and coefficient in terms, match terms to their equivalents, and understand the concept of equivalent expressions. Practice simplifying and identifying like terms with the help of visual models and examples provided. Strengthen your algebra skills and learn how to recognize and combine similar terms effectively.
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Presentation Transcript
1) Match the terms on the left with the equivalent card on the right. ?2 2 ? 2? 2 ? ? 2?2 ? ? 2?2 2 ? 2 ? 2) In the term 3?, the letter ? is the __________ . 3) In a the term 3?, the number 3 is called the ___________ of ?. 4) Which expression is represented by the bar model? ? 7 ? 7 ? 7 3(? + 7) 3? + 7 3(? + 21) 3? + 21
1) Match the terms on the left with the equivalent card on the right. ?2 2 ? 2? 2 ? ? 2?2 ? ? 2?2 2 ? 2 ? variable 2) In the term 3?, the letter ? is the __________ . 3) In a the term 3?, the number 3 is called the ___________ of ?. coefficient 4) Which expression is represented by the bar model? ? 7 ? 7 ? 7 3(? + 7) 3? + 7 3(? + 21) 3? + 21
Two expressions are equivalent if they are equal for all values of the variables in each expression. 3(? + 7) 3? + 21 ? 5 10 0.1 7 ? 5 10 0.1 7 ? 5 10 0.1 7 ? 5 10 0.1 ? 5 10 0.1 ? 5 10 0.1 7 7 7 3 + 7 = 3 0.1 +21 10 10 0.1 5 5 36 = 36 51 = 51 21.3 = 21.3
Simplify a + a + a + a + a 5a a a a a a 5a
And another 3c + 2c + c 6c 3c 2c c 6c
Simplifying Expressions: Discuss: Which of these expressions contain a pair of like terms? How do you know? ???+ ??? ?? + ?? ? ? + ? ?
3? + 3? Like / Unlike 3? 3? Like / Unlike In pairs: 3? 2? Like / Unlike Decide which expressions contain ONLY like terms 3? 2? Like / Unlike 5? 2? Like / Unlike Extend: Can you write the simplified expression using the identity symbol for the expressions with like terms? 5?2 2? Like / Unlike 5?2 2?2 Like / Unlike 5?2+ 2?2 Like / Unlike 5?2+ 2?2 Like / Unlike
5?2+ 2?2 Like / Unlike 5? 2+ 2? 2 5? 2+ 2? 2 Like / Unlike Like / Unlike 5? 2+ 2? 3 Like / Unlike 5? 2+ 2? 3 ? Like / Unlike 5? 4+ 2? 4 ? 4 Like / Unlike 5? 4.7+ 2? 4.7 ? 4.7 Like / Unlike 4 7+ 2? 4 7 ? 4 7 5? Like / Unlike 4 7+ 2? 4 7 ? 4 7 Like / Unlike 5?
5 ? + 2 ? ? Like / Unlike 5 ? + 2 ? ? Like / Unlike 5? + 2 ? ? Like / Unlike 5? + 2 ? ?2 Like / Unlike
3? + 3? Like / Unlike 3? 3? Like / Unlike 3? 2? Like / Unlike 3? 2? Like / Unlike 5? 2? Like / Unlike 5?2 2? Like / Unlike 5?2 2?2 Like / Unlike 5?2+ 2?2 Like / Unlike 5?2+ 2?2 Like / Unlike
5?2+ 2?2 Like / Unlike 5? 2+ 2? 2 Like / Unlike 5? 2+ 2? 2 Like / Unlike 5? 2+ 2? 3 Like / Unlike 5? 2+ 2? 3 ? Like / Unlike 5? 4+ 2? 4 ? 4 Like / Unlike 5? 4.7+ 2? 4.7 ? 4.7 Like / Unlike 4 7+ 2? 4 7 ? 4 7 5? Like / Unlike 4 7+ 2? 4 7 ? 4 7 Like / Unlike 5?
5 ? + 2 ? ? Like / Unlike 5 ? + 2 ? ? Like / Unlike 5? + 2 ? ? Like / Unlike 5? + 2 ? ?2 Like / Unlike
Collecting like terms Like terms are terms whose variables (and their powers such as the 2 in x2) are the same. The coefficients may be different. Algebraic expressions can be simplified by collecting like terms
Simplify 4d + d + d d 5d 4d d d -d 5d
And another 3e2 e2 + 2e2 2e2 e2 3e2
And another 2a + 3b + 4a + b 6a + 4b 2a 3b 4a b 2a 4a 3b b 3b b 2a 4a 6a + 4b
And another -2a - 3b + 4a + b 2a 2b 4a b -2a -3b
On your whiteboards Simplify the following expressions by collecting like terms.
4d + d + 3d 8d
5d -2d + 3d 6d
5p + 4q 2p + q 3p + 5q
2p2 +3p2 4p2 p2
3pq - 4 + 5pq 8pq - 4
Worked Example Your Turn ????????3? + 4? + 2? ? 2p 3p 4? ? Working out: 3? + 2? = 5? 4? ? = 3? Answer: 5? + 3?
In your books, fully simplify each expression 1. ? + ? + 2? + 3? 2. 2? + 3? + ? + 8? 3. 3? + ? + 4? + 2? 4. 5? + 9? + 4? + 6? 5. ? + 8? + 2? + ? 6. 4? + ? + 3? + 2? 7. 3? + 3? + 7? 3? 8. 8? + 3? 6? + 2? 9. 2?2 ?? + 3?2 + 4?? 4?2 ?2 10. 1 2??2 2??2+3 4??2
Mark your work 1. 1. 3? + 4? 2. 2.3? + 11? 3. 3.6? + 4? 4. 4.9? + 15? 5. 5.3? + 9? 6. 6.8? + 2? 7. 7.6? + 4? 8. 2? + 5? 9. ?2+ 3?? ?2 10. ??2
