4. Determine the pattern
1 = 12 These are perfect squares!
4 = 22 You should be able to list
9 = 32 the first 15 perfect
squares in 30 seconds…
16 = 42
25 = 52
Perfect squares
36 = 62 1, 4, 9, 16, 25, 36, 49, 64, 81,
… 100, 121, 144, 169, 196, 225
6. Factoring Chart
This chart will help you to determine
which method of factoring to use.
Type Number of Terms
1. GCF 2 or more
2. Diff. Of Squares 2
3. Trinomials 3
7. Review: Multiply (y + 2)2
Do you remember these?
(y + 2)(y + 2) (a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 – 2ab + b2
First terms: y2
Using the formula,
Outer terms: +2y (y + 2)2 = (y)2 + 2(y)(2) + (2)2
Inner terms: +2y (y + 2)2 = y2 + 4y + 4
Last terms: +4 Which one is quicker?
Combine like terms.
y2 + 4y + 4
8. 1) Factor x2 + 6x + 9 Perfect Square Trinomials
(a + b)2 = a2 + 2ab + b2
Does this fit the form of our (a - b)2 = a2 – 2ab + b2
perfect square trinomial?
2) Is the first term a perfect
square?
Yes, a = x
2) Is the last term a perfect Since all three are true,
square? write your answer!
Yes, b = 3 (x + 3)2
6) Is the middle term twice the
product of the a and b?
You can still
Yes, 2ab = 2(x)(3) = 6x factor the other way
but this is quicker!
9. 2) Factor y2 – 16y + 64 Perfect Square Trinomials
(a + b)2 = a2 + 2ab + b2
Does this fit the form of our (a - b)2 = a2 – 2ab + b2
perfect square trinomial?
2) Is the first term a perfect
square?
Yes, a = y
2) Is the last term a perfect Since all three are true,
square? write your answer!
Yes, b = 8 (y – 8)2
6) Is the middle term twice the
product of the a and b?
Yes, 2ab = 2(y)(8) = 16y
10. 3) Factor 4p2 + 4p + 1 =(2p + 1)2
Does this fit the form of our Perfect Square Trinomials
perfect square trinomial? (a + b)2 = a2 + 2ab + b2
2) Is the first term a perfect (a - b)2 = a2 – 2ab + b2
square?
Yes, a = 2p
2) Is the last term a perfectSince all three are true,
square? write your answer!
Yes, b = 1 (2p + 1)2
6) Is the middle term twice the
product of the a and b?
Yes, 2ab = 2(2p)(1) = 4p
11. 4) Factor 25x2 – 110xy + 121y2
Does this fit the form of our perfect
square trinomial? Perfect Square Trinomials
(a + b)2 = a2 + 2ab + b2
2) Is the first term a perfect (a - b)2 = a2 – 2ab + b2
square?
Yes, a = 5x
4) Is the last term a perfect Since all three are true,
square? write your answer!
Yes, b = 11y (5x – 11y)2
6) Is the middle term twice the
product of the a and b?
Yes, 2ab = 2(5x)(11y) = 110xy
This template can be used as a starter file for presenting training materials in a group setting. Sections Right-click on a slide to add sections. Sections can help to organize your slides or facilitate collaboration between multiple authors. Notes Use the Notes section for delivery notes or to provide additional details for the audience. View these notes in Presentation View during your presentation. Keep in mind the font size (important for accessibility, visibility, videotaping, and online production) Coordinated colors Pay particular attention to the graphs, charts, and text boxes. Consider that attendees will print in black and white or grayscale. Run a test print to make sure your colors work when printed in pure black and white and grayscale. Graphics, tables, and graphs Keep it simple: If possible, use consistent, non-distracting styles and colors. Label all graphs and tables.
This template can be used as a starter file for presenting training materials in a group setting. Sections Right-click on a slide to add sections. Sections can help to organize your slides or facilitate collaboration between multiple authors. Notes Use the Notes section for delivery notes or to provide additional details for the audience. View these notes in Presentation View during your presentation. Keep in mind the font size (important for accessibility, visibility, videotaping, and online production) Coordinated colors Pay particular attention to the graphs, charts, and text boxes. Consider that attendees will print in black and white or grayscale. Run a test print to make sure your colors work when printed in pure black and white and grayscale. Graphics, tables, and graphs Keep it simple: If possible, use consistent, non-distracting styles and colors. Label all graphs and tables.
