# What is the standard form of y= (x+3)(1-3x)-7x?

Dec 9, 2015

$y = - 3 {x}^{2} - 15 x + 3$

#### Explanation:

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
To demonstrate what is happening:
Consider the product $2 \times 3$

We all know that the answer is 6.

We also know that $2 \times 3$ is in fact saying 2 of 3 in that we have

$2 \times 3 = 3 + 3 = \textcolor{b l u e}{3} \times \textcolor{red}{2}$

But what if we wrote 3 as $\textcolor{b l u e}{2 + 1}$

This is still so $\textcolor{b l u e}{\left(2 + 1\right)} \textcolor{red}{\times 2} = 6$

The distributive property of multiplication simply means that we can write this as:color(blue)((2color(red)(xx2))+(1color(red)(xx2))
Can you see the way that multiplication by the 2 is 'spread around' (that is not a math term!!)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Doing the same thing with your question:

Given:$\textcolor{w h i t e}{. .} \textcolor{g r e e n}{y = \textcolor{b l u e}{\left(x + 3\right)} \textcolor{red}{\left(1 - 3 x\right)} - 7 x}$

Consider just the brackets part:

Write as color(blue)(x color(red)((1-3x))+3color(red)((1-3x))

This becomes: $x - 3 {x}^{2} + 3 - 9 x$

Putting it all together:

$\textcolor{w h i t e}{. .} \textcolor{g r e e n}{y = \textcolor{b l a c k}{x - 3 {x}^{2} + 3 - 9 x} - 7 x}$

Collecting like terms gives:

$\textcolor{g r e e n}{y = - 3 {x}^{2} - 15 x + 3}$

It just takes a little practice that is all!