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Learning Algebra Amber Elsner 8 th Grade Algebra Click for the next slide

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Algebraic Expressions Distributive Properties Graphing Combining Like Terms Multiplying Monomials Multiplying Binomials: FOIL (smiling man) Solving Equations Multiplying Binomials: Box Method Algebra Topics Review Question CLICK either the text or image to learn each algebra topic!

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Algebraic Expressions Equation- a complete math sentence that includes an equal sign Expression- a math sentence without an equal sign Terms- separate values in an expression Variable- unknown number, often represented by “x” Constant- a number that doesn’t change Coefficient- number that is multiplied by the variable Equation- a complete math sentence that includes an equal sign Expression- a math sentence without an equal sign Terms- separate values in an expression Variable- unknown number, often represented by “x” Constant- a number that doesn’t change Coefficient- number that is multiplied by the variable Click to go back to Algebra Topics = 2 Monomial- 1 term Ex: (xy) Binomial- 2 terms Ex: (xy – zx) Trinomial- 3 terms Ex: (xy – zx + 4y) Quadnomial- 4 terms Ex: (xy – zx + 4y – 3) Monomial- 1 term Ex: (xy) Binomial- 2 terms Ex: (xy – zx) Trinomial- 3 terms Ex: (xy – zx + 4y) Quadnomial- 4 terms Ex: (xy – zx + 4y – 3)

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Combining Like Terms Add or Subtract integers, combine coefficients Keep operations with correct terms o 4x - 7x -3x Order of the terms does not matter Example: 3y + 2x - 9y (combine 3y and -9y) 2x - 6y (another way to write it) -6y + 2x Add or Subtract integers, combine coefficients Keep operations with correct terms o 4x - 7x -3x Order of the terms does not matter Example: 3y + 2x - 9y (combine 3y and -9y) 2x - 6y (another way to write it) -6y + 2x Click to go back to Algebra Topics

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Distributive Properties Click to go back to Algebra Topics Note: These do not work with subtraction or division. Distribute the x to the y and the z x (y + z) = xy + xz x (y – z) = xy – xz Note: that the (+) and (–) signs separate the xy and the xz when the x is distributed Distribute the x to the y and the z x (y + z) = xy + xz x (y – z) = xy – xz Note: that the (+) and (–) signs separate the xy and the xz when the x is distributed

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Multiplying Monomials Click to go back to Algebra Topics

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Multiplying Binomials: FOIL (smiling man) FOIL stands for: – F: multiply the first terms in each factor (x – 2)(2x + 1) – O: multiply the outside terms in each factor (x – 2)(2x + 1) – I: multiply the inside terms in each factor (x – 2)(2x + 1) – L: multiply the last terms in each factor (x – 2)(2x + 1) FOIL stands for: – F: multiply the first terms in each factor (x – 2)(2x + 1) – O: multiply the outside terms in each factor (x – 2)(2x + 1) – I: multiply the inside terms in each factor (x – 2)(2x + 1) – L: multiply the last terms in each factor (x – 2)(2x + 1) Click to go back to Algebra Topics Result from FOIL: 2x² + x – 4x – 2 Simplify: 2x² – 3x – 2 Result from FOIL: 2x² + x – 4x – 2 Simplify: 2x² – 3x – 2

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Multiplying Binomials: Box Method Create a two-by-two box – One factor goes on top – The other goes on the side – Signs should stay with the correct number and variable Create a two-by-two box – One factor goes on top – The other goes on the side – Signs should stay with the correct number and variable Click to go back to Algebra Topics X X 2 + - 4 Multiply each factor in rows and in columns ‒Top left box: x² ‒Top right box: -2x ‒Bottom left box: 4x ‒Bottom right box: -8 Multiply each factor in rows and in columns ‒Top left box: x² ‒Top right box: -2x ‒Bottom left box: 4x ‒Bottom right box: -8 Add together each term x² + 4x – 2x – 8 Combine like terms x² + 2x – 8 Add together each term x² + 4x – 2x – 8 Combine like terms x² + 2x – 8

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Graphing Use two axes – Horizontal x-axis – Vertical y-axis When x and y axes meet they form 4 quadrants – Labeled 1 to 4 in Roman numerals Quadrant I is in top right Quadrant II is in top left Quadrant III is in bottom left Quadrant IV is in bottom right – If a point is on the x or y axes, then that point is not located in any quadrant. Use two axes – Horizontal x-axis – Vertical y-axis When x and y axes meet they form 4 quadrants – Labeled 1 to 4 in Roman numerals Quadrant I is in top right Quadrant II is in top left Quadrant III is in bottom left Quadrant IV is in bottom right – If a point is on the x or y axes, then that point is not located in any quadrant. Click to go back to Algebra Topics Plotting points – Written as (x, y) Always start at the origin – Center point of the graph (0, 0) Find the position on the x-axis Locate the position on the y-axis Plot where the two meet Plotting points – Written as (x, y) Always start at the origin – Center point of the graph (0, 0) Find the position on the x-axis Locate the position on the y-axis Plot where the two meet

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Solving Equations Whatever you do to one side you MUST do to the other side – Why? To keep each side balanced! Whatever you do to one side you MUST do to the other side – Why? To keep each side balanced! Click to go back to Algebra Topics Isolate variables by using opposite operations – Addition: use subtraction x + 1 = 5 - 1 - 1 x = 4 – Subtraction: use addition x – 2 = -6 + 2 + 2 x = -4 Isolate variables by using opposite operations – Addition: use subtraction x + 1 = 5 - 1 - 1 x = 4 – Subtraction: use addition x – 2 = -6 + 2 + 2 x = -4 – Multiplication: use division 3x = 21 3 3 x = 7 – Division: use multiplication x/3 = 5 * 3 x = 15 – Multiplication: use division 3x = 21 3 3 x = 7 – Division: use multiplication x/3 = 5 * 3 x = 15

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REVIEW QUESTION! What is the correct, simplified answer when you multiply the binomial (2x – 2)(x + 5) ? A. 2x² – 8x – 102x² – 8x – 10 B.2x² + 8x – 102x² + 8x – 10 C.2x² + 12x + 102x² + 12x + 10

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2x² – 8x – 10 Click to go back to Review Question Watch the signs when using the distributive property and multiplying the numbers. Check your work and go back to try again

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Click to continue 2x² + 8x – 10 Correct! Great work! You multiplied the binomial and simplified it correctly!

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Click to go back to Review Question Watch the signs when using the distributive property and multiplying the numbers. 2x² + 12x + 10 Check your work and go back to try again

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Congratulations! You have successfully completed learning some basic algebra concepts! Click ALGEBRA to return to the title slide for the next student:

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