Algebra Toolkit

1. We factor out a common factor of \(4x\) to get \(4x(x-1)\text{.}\)

2. This is a difference of two squares that factors as \((2x-1)(2x+1)\text{.}\)

3. This is the square of a binomial, \((2x-1)^2\text{.}\)

1. We first factor out 3 to find \(3(9a^2-1)\text{,}\) then factor the difference of two squares to get \(3(3a-1)(3a+1)\text{.}\)

2. This is a differece of two cubes, which factors as \((3a-1)(9a^2+3a+1)\text{.}\)

3. We first factor out \(a\) to get \(a(81a^2-1)\text{,}\) then factor the difference of two squares to get \(a(9a-1)(9a+1)\) .

The opposite of \(m^2-p\) is \(-(m^2-p) = -m^2+p\text{,}\) or \(p-m^2\text{.}\)

The opposite of \(5c-3\) is \(-(5c-3)=-5c+3\text{,}\) or \(3-5c\text{,}\) so (c) is correct.

This line is a vertical line. All the points on the line have \(x\)-coordinate \(-15\text{,}\) so the equation of the line is \(x=-15\text{.}\) Because \(\Delta x=0\) between any two points on the line, its slope is undefined.

This line is a horizontal line. All the points on the line have \(y\)-coordinate \(04\text{,}\) so the equation of the line is \(y=40\text{.}\) Because \(\Delta y=0\) between any two points on the line, its slope is \(0\text{.}\)