Algebra: Chapter 6, Lesson 3, page 270
Trinomial Squares
We are going backward again, using the properties:
- `(a + b)(a + b) = a^2 + 2ab + b^2 = (a + b)^2`
- `(a – b)(a – b) = a^2 – 2ab + b^2 = (a – b)^2`
For a trinomial square to factor, we must make sure that:
- 2 of the terms must be squares, `a^2` and `b^2`
- There must be NO MINUS sign before the `a^2` and `b^2`
- If we multiply `a` and `b` and double the result, we get the 3rd term, `2ab` or its additive inverse `- 2ab`.
Sometimes, we can also factor out a coefficient in front of the `a^2`, like `2a^`. We MIGHT be able to factor out the `2` before we start the trinomial determination.
Here is a purplemath link that describes trinomial squares, scroll down about 1/2 way to get to the information.
Two of tonight’s homework problems solved by MrE are here! Just click it!
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Algebra 1a: Chapter 7, Lesson 4, page 318.
Slope of a Line
The slope of a line is the tilt or slant. The slope is defined as the letter `m` and `m=(rise)/(run)`, where the `rise` is the change in the y-coordinate and the `run` is the change in the x-coordinate. This definition works great when you have 2 points on graph paper. You can just count the squares for the rise and the run. It doesn’t matter too, which point you start with.
Remember, slope is positive if the line is going from lower left to upper right. The slope is negative if its coming from upper left to lower right.
A slope of `0` is a horizontal line and a line with NO SLOPE is a vertical line.
Another definition of slope, given 2 point and NO GRAPH PAPER is:
`m=(y_2−y_1)/(x_2−x_1)`, where `(x_1,y_1)` and `(x_2,y_2)` are 2 points on the line.
For example, for the points (2, -3) and (-4, 2), the slope is:
`m = (2 – (-3))/(-4 – 2) = 5/(-6) = -(5/6)`
Purplemath has this link as well.
Two of tonight’s homework problems solved by MrE are here! Just click it.