Algebra: Chapter 6, Lesson 2, page 266.
Difference of 2 squares
For a binomial to be a difference of 2 squares, 2 conditions must be met.
- There must be 2 terms, both must be square (e.g., `4x^2` and `9x^4`)
There must be a minus sign `(-)` between the 2 terms.
We are going backward in our factoring, using our first Chapter 5 shortcut formula:
`a^2 – b^2 = (a + b)(a – b)`,
so once we have the 2 squares, just plug them in to our formula!
Examples:
`9a^8b^4 – 49 = (3a^4b^2)^2 – 7^2`
`= (3a^4b^2 + 7)(3a^4b^2 – 7)`
and another example where we have to factor something out first, namely `x^4`, we have:
`49x^4 – 9x^6 = x^4(49 – 9x^2) `
`= x^4[7^2 – (3x)^2]`
with the final factors being = `x^4(7 +3x)(7 – 3x)`
Two of tonight’s homework problems solved by MrE are here! Just click it!
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Algebra 1a: Chapter 7, Lesson 3, page 313.
Linear Equations and their Graphs
Linear equation have to have variables with a power of 1, NO mixed variable products and NO variables in an equation in the denominator. The easiest way to plot or graph an equation is to use the x-intercept and y-intercept.
- The x-intercept of a line is the x-coordinate of the point where the line intercepts the x-axis. To do this, all we have to do is set `y=0` and solve for `x`.
- The y-intercept of a line is the y-coordinate of the point where the line intercepts the y-axis. To do this, set `x=0` and solve for `y`
The standard form of a linear equation in 2 variables is `Ax + By = C`, where A, B and C are constants.
For horizontal lines, the graph of `y = b` is the x-axis or a line parallel to the x-axis with y-intercept, `b`.
For vertical lines. the graph of `x = a` is the y-axis or a line parallel to the y-axis with x-intercept, `a`.
Two of tonight’s homework problems solved by MrE are here! Just click it.