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

1 Answer
Dec 9, 2015

#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!