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Slideshow 9, Mathematics Mr Richard Sasaki
Collecting Like Terms Slideshow 9, Mathematics Mr Richard Sasaki
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Objectives Recall Algebraic Operations and notation
To gather numbers and unknowns To simplify expressions with various unknowns
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Algebraic Operations Simplify the followingβ¦ 2Γπ₯ 2π₯ = π₯+π₯ 2π₯ = π₯Γπ¦ π₯π¦
π₯ 2 + π₯ 2 2 π₯ 2 = π₯Γπ₯ π₯ 2 = π₯+π¦ π₯+π¦ = 5π₯ 3 or 5 3 π₯ Note: 5Γ·3 Γπ₯= . We shouldnβt writeβ¦ 1 2π₯ 3 or π₯ Decimal numbers like 1.2π₯ are fine!
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Vocabulary Letβs look at some components of the expression below. Why 6π₯? 4π₯+2π₯ 6π₯ = We did 2+4=6. Operator (Plus) Coefficients Coefficients - Numbers that appear in front of unknowns. Operator - Symbols like +,β,Γ,Γ·, , that allow us to perform calculations. Symbols like % or # are not operators (in mathematics).
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Collecting Like Terms 4π₯+ π₯ = 5π₯ 1
Both 4π₯ and 2π₯ have the like term π₯. We can add the π₯ terms together (or subtract) as they are the same thing. So 4π₯+2π₯=6π₯. Calculate 2 bananas + 4 bananas. 6 bananas It doesnβt matter if we add unknowns, bananas, objects, or numbers, we can collect them together. 4π₯+ π₯ = 5π₯ 1 Here, we did the calculation 4+1=5. Where did the 1 come from? We donβt usually write the coefficient 1 though.
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Collecting Like Terms 4π₯+3π¦ 4π₯+3π¦ =
Letβs try some terms that are not like terms. 4π₯+3π¦ 4π₯+3π¦ = Can we add bananas to coconuts to make some magical banana coconuts? No! We canβt add π₯ to π¦ either. We can only combine like terms. So we just leave it the same. Note: If a question says simplify π₯+π¦, write π₯+π¦. If you write nothing youβll get it wrong.
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Collecting Like Terms + 5π₯+2π¦+6π₯= 5π₯+6π₯+2π¦ =11π₯+2π¦ 2π₯+3π¦βπ¦+4π₯=
Examples Note: We can rearrange. π+π=π+π. Simplify 5π₯+2π¦+6π₯. 5π₯+2π¦+6π₯= 5π₯+6π₯+2π¦ =11π₯+2π¦ Simplify 2π₯+3π¦βπ¦+4π₯. + 2π₯+3π¦βπ¦+4π₯= 2π₯+4π₯+3π¦βπ¦ =6π₯+2π¦ Note: The first term is positive unless there is a minus symbol.
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Collecting Like Terms β7π₯+9π¦β5π¦+2π§= β7π₯+4π¦+2π§ Example
Simplify β7π₯+9π¦β5π¦+2π§. β7π₯+9π¦β5π¦+2π§= β7π₯+4π¦+2π§ It is usually better to write terms in alphabetical order. Notice the first term above is π₯, then π¦ and lastly, π§. There is one exception however for binomials (an expression with two terms)β¦ It is preferable to write βπ₯+π¦ as π¦βπ₯ To some people, it looks untidy to start with β.
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8π¦ 2π¦ 7π₯ π¦ 4π₯ 11π¦ 10π₯ 6π₯ 8π₯+3π¦ 3π₯+8π¦ 7π₯β4 2π¦+10 3π₯+2π¦ 6π₯+5π¦ 11π₯+2π¦ 8π₯+3π¦ 2π§β2π¦ 14π¦ β4π₯ 10π₯+5π¦β7π§ 2π+3πβ3 3π₯β3π¦ 3π¦βπ₯ βπ₯β3 3.8π¦β2π₯ 2π¦β101π₯ 4π₯ π₯ 29π₯ 35 3π₯ 4
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Other Forms As you know, π₯ is an unknown. In the same way, π₯ 2 is an unknown, especially if we donβt know π₯. For this reason, we can add and subtract like terms for π₯ 2 or π₯ 3 together (but not with each other). Note: π₯ 3 is read π₯ cubed. Example Simplify π₯ 3 + π₯ 2 +2 π₯ 3 . π₯ 3 + π₯ 2 +2 π₯ 3 = 3 π₯ 3 + π₯ 2 Note: Terms should be ordered β¦+ π₯ 3 + π₯ 2 +π₯+π.
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2 π₯ 3 π₯ 3 +2 π₯ 2 3 π₯ 2 βπ₯ 5 π¦ 2 β4π¦ 5 π₯ 2 +2π₯β3 7 π₯ 6 +2 π₯ 4 2π₯β4 π₯ 2 3 π₯ 2 β π₯ 3 π₯ 2 +3 3ππ ππ π₯π¦ π 2 π 3π π 2 +2ππ 8π₯ π π 2 4π₯+9π¦ 4π₯+5π¦+4π§
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2 π 2 πβπ π 2 3ππβ3π+2 β3 π 2 β4π+10 2ππ 6 β4 π 2 β2π 6 π₯ 2 βπ₯ 4ππ+π π 2 34 π₯ 2 β42 6 π 7 β6 π β7 2 π₯ 2 β5 4π₯ π¦ 2 +13π₯π¦ 3 π₯ 2 +7 π₯ 2 +7π₯ 8π₯π¦β6π₯+π¦ 9 π 2 β2π 12 π₯ 2 π π 2 24π₯ ππ
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