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

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!

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)

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

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

Multiplying Monomials Click to go back to Algebra Topics

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

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 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

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

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 = x = 4 – Subtraction: use addition x – 2 = x = -4 Isolate variables by using opposite operations – Addition: use subtraction x + 1 = x = 4 – Subtraction: use addition x – 2 = x = -4 – Multiplication: use division 3x = x = 7 – Division: use multiplication x/3 = 5 * 3 x = 15 – Multiplication: use division 3x = x = 7 – Division: use multiplication x/3 = 5 * 3 x = 15

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

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

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

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

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