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Chapter 3 - Expressions

Chapter 3 - Expressions

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Mathematics

•

7th Grade

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Hard

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Heather Chambers

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16 Slides • 17 Questions

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Chapter 3 - Algebraic Expressions

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Simplifying Algebraic Expressions

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Example


 9x−2+7−x9x-2+7-x  

Rewrite as a sum of terms:  9x+(−2)+7+(−x)9x+\left(-2\right)+7+\left(-x\right)  
Terms:  9x, −2, 7, −x9x,\ -2,\ 7,\ -x  
Like Terms:  9x and −x, 7 and −29x\ and\ -x,\ 7\ and\ -2  
Simplified:  8x+58x+5  

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Another Example

 6n−10n=(6−10)n6n-10n=\left(6-10\right)n  Distributive Property
 =−4n=-4n  Subtract

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Adding and Subtracting Linear Expressions

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Vocabulary

  • Linear Expression - an algebraic expression where the exponent of each variable is 1.

  • Linear Expressions:

     −4x, 3x+5y, 5−16x-4x,\ 3x+5y,\ 5-\frac{1}{6}x  

  • Nonlinear Expressions:  12x2, −7x3+x, x5+1\frac{1}{2}x^2,\ -7x^3+x,\ x^5+1  

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Adding Expressions Example


 (x−2)+(3x+8)\left(x-2\right)+\left(3x+8\right)  

Rewrite the sum:  −4y+3+11y−5-4y+3+11y-5  
Use the Commutative Property of Addition:  −4y+11y+3−5-4y+11y+3-5  
Group like terms:  (−4y+11y)+(3−5)\left(-4y+11y\right)+\left(3-5\right)  
Combine like terms:  7y−27y-2  

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Subtracting Expressions Example

 (5x+6)−(−x+6)\left(5x+6\right)-\left(-x+6\right)  


Add the opposite:  (7y+5)+(−8y+6)\left(7y+5\right)+\left(-8y+6\right)  
Use the Commutative Property of Addition: 7y+(−8y)+5+67y+\left(-8y\right)+5+6  
Group Like terms:  [7y+(−8y)]+(5+6)\left[7y+\left(-8y\right)\right]+\left(5+6\right)  
Combine Like Terms:  −y+11-y+11  

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The Distributive Property

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Example


 −13(3n−6)-\frac{1}{3}\left(3n-6\right)  

Use the distributive property:  −13(3n)−(−13)(6)-\frac{1}{3}\left(3n\right)-\left(-\frac{1}{3}\right)\left(6\right)  
Multiply:  −n−(−2)-n-\left(-2\right)  
Add the opposite:  −n+2-n+2  

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Another Example


 −3(−1+2x+7)-3\left(-1+2x+7\right)  

Distributive Property:  −3(−1)+(−3)(2x)+(−3)(7)-3\left(-1\right)+\left(-3\right)\left(2x\right)+\left(-3\right)\left(7\right)  
Multiply: 3+(−6x)+(−21)3+\left(-6x\right)+\left(-21\right)  
Combine Like Terms:  −6x−18-6x-18  

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Factoring Expressions

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Vocabulary

  • Factoring an Expression: Writing an algebraic expression as a product of factors.

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Example


 24x−1824x-18  Factoring Out GCF


Find GCF:  24x: 1, 2, 3, 4, 6, 8, 12, 24, x24x:\ 1,\ 2,\ 3,\ 4,\ 6,\ 8,\ 12,\ 24,\ x  
 18: 1, 2, 3, 6, 9, 1818:\ 1,\ 2,\ 3,\ 6,\ 9,\ 18  
GCF: 6
Rewrite using GCF:  6(4x)−6(3)6\left(4x\right)-6\left(3\right)  
Distributive Property:  6(4x−3)6\left(4x-3\right)  

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Another Example


Factoring out a Rational number:
Factor  12\frac{1}{2}  out of  12x+32\frac{1}{2}x+\frac{3}{2}  


 12(x)++12(3)\frac{1}{2}\left(x\right)++\frac{1}{2}\left(3\right)  Rewrite the expression
 12(x+3)\frac{1}{2}\left(x+3\right)  Distributive Property

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Yet Another Example


Factoring Out a negative Number: Factor -2 out of  −4p+10-4p+10  .


Rewrite the expression:  −2(2p)+(−2)⋅(−5)-2\left(2p\right)+\left(-2\right)\cdot\left(-5\right)  
Distributive Property:  −2[2p+(−5)]-2\left[2p+\left(-5\right)\right]  
Simplify:  −2(2p−5)-2\left(2p-5\right)  

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Chapter 3 - Algebraic Expressions

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Modeling with mathematics
Understanding key terms
Calculating/Estimating and interpreting the average rate of change
Rewriting Expressions Using Structure
Writing a(x)/b(x) in the form of q(x) + r(x)/b(x), with the degree of r(x) less than the degree of b(x) using the long division algorithm
Solving problems involving nth roots
Generating and understanding linear equations in one variable with no solution
Graphing Symbolic Quadratic Functions
Designing and building
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