Factorise 3(2x+3y)² - 8x - 12y

Factorise 3(2x + 3y)^2 - 8x - 12y

First, we FOIL it.

FOIL: First, Outside, Inside, and Last

(2x + 3y)(2x + 3y)

First: 2x*2x = 4x^2

Outside: 2x*3y = 6xy

Inside: 3y*2x = 6xy

Last: 3y*3y = 9y^2

Before, we move on, we have to combine any like terms.

6xy + 6xy = 12xy

Then, when we've finished FOILing it, we place a pair of parentheses around these.

3 (9y^2 + 4x^2 + 12xy) -8x - 12y

Now, we can distribute the 3.

3 * 9y^2 = 27y^2

3 * 4x^2 = 12x^2

3 * 12xy = 36xy

Lastly, we combine any like terms if there are any.

Expression: 27y^2 + 12^2 + 36xy - 8x - 12y

None of these all have a greatest common factor for the whole set.

So, therefore, the factorised form of 3(2x + 3y)^2 - 8x - 12y is:

27y^2 + 12x^2 + 36xy - 8x - 12y

Step-by-step explanation:

Our first step is to use the perfect square formula:

() Where and

We are using this so we can simplify what's in the parenthesis because it's being squared.

Let's start!

Using PEMDAS we must multiply first.

This is equal to

Now  we will have solve for the rest of the equation

The new equation (inside of the parenthesis) is equal to:

The full equation looks like

Now we will Distribute!

Using foil we will multiply the numbers in the parenthesis by 3.

Now our equation looks like:

That is all we can do to factor.

Thus, the answer is  

the co-ordinates of the transformed rectangle are:

d. (0, 0), (0, 3), (-3, 3), (-3, 0)

step-by-step explanation:

from the columns of the given matrix, the co-ordinates of the rectangle before transformation are:

(0, 0), (0, 3), (3, 3), (3, 0)

r =

transformed matrix can be obtained by multiplying the given matrix by r:

columns of the transformed matrix are:

0   0   -3   -3

0   3     3     0

from the columns of the resulted matrix, we can see that the vertices of the transformed triangle are:

(0, 0), (0, 3), (-3, 3), (-3, 0)