Question

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

Answer 1

`y= -3x^2-15x+3`

Explanation:

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To demonstrate what is happening:
Consider the product `2xx3`

We all know that the answer is 6.

We also know that `2xx3` is in fact saying 2 of 3 in that we have

`2xx3 = 3+3 =color(blue)(3)xx color(red)(2)`

But what if we wrote 3 as `color(blue)(2+1)`

This is still so `color(blue)((2+1)) color(red)(xx2)=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!!)
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Doing the same thing with your question:

Given:`color(white)(..)color(green)(y=color(blue)((x+3)) color(red)((1-3x))-7x)`

Consider just the brackets part:

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

This becomes: `x-3x^2+3-9x`

Putting it all together:

`color(white)(..)color(green)(y=color(black)(x-3x^2+3-9x)-7x)`

Collecting like terms gives:

`color(green)(y= -3x^2-15x+3)`

It just takes a little practice that is all!