Question

Factorise 3(2x+3y)² - 8x - 12y​

Answer 1

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

Answer 2

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

Explanation:

Our first step is to use the perfect square formula:

(
`\left(a+b\right)^2=a^2+2ab+b^2`) Where
`a=2x` and
`b=3y`

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

Let's start!

`(2x+by)^2= 2^2x+2(2x)(3y)+ 3^2y`

Using PEMDAS we must multiply first.

`2*2x *3y`

This is equal to

`12xy`

Now we will have solve for the rest of the equation

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

`(4x^2+12xy+9y^2)`

The full equation looks like

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

Now we will Distribute!

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

Now our equation looks like:

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

That is all we can do to factor.

Thus, the answer is
`12x^2+36xy+27y^2-8x-12y`