factor the diffrence of squares? Whats the answer for 25k^2-9 and 16x^2-40x+25

Question

mathstudent55 · Answer

The first one is a difference of squares.
The second one is not a difference of squares.

For a difference of squares:
$a^2 - b^2 = (a + b)(a - b) $

anonymous · Answer

I still dont get it

mathstudent55 · Answer

Look at this term:

$x^2$

Obviously, $x^2$ is the square of x.

A term that is a square can be more complicated. 

For example,

$4x^2$ is the square of 2x.

$9y^2$ is the square of 3y.

blackops2luvr · Answer

49?

anonymous · Answer

for the first one I got 625^2-450k+81

mathstudent55 · Answer

A difference means a subtraction.
A difference of squares is a square being subtracted from a square.

Look at your first problem,

$25k^2 - 9$

Notice that $25k^2$ is the square of 5k.
9 is the square of 3.

Since 9 (a square) is being subtracted from $25k^2$ (also a square), you have a subtrtaction of squares, or a difference of two squares.

mathstudent55 · Answer

To factor a difference of squares, follow this pattern:

$a^2 - b^2 = (a + b)(a - b) $

$25k^2 - 9$

$= (5k)^2 - (3)^2$

In the line above, you see more clearly that it's the difference of two squares.

Now follow the pattern.

$ = (5x + 3)(5k - 3) $