How do you simplify #6(-5n+7)#?

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Answer 1 · 2016-04-24T15:24:43

#-30n+42#

Given:#" "6(-5n+7)#

#color(red)("Shortcut method: Multiply everything inside the brackets by 6")#

#color(blue)(-30n+42)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(red)("Explaining what is really happening.")#

Consider the word phrase "2 apples". This is the same as "2 of apples". Mathematically you could write: #2xx#apples or even 2a.

This is exactly the type of thing you have when you write:#" "6(-5n+7)#

This is the same as: #6" of "(-5n+7)#

Lets write this out in full:

#(-5n+7)+(-5n+7)+(-5n+7)+(-5n+7)+(-5n+7)+(-5n+7)#

Write this as:

#(-5n-5n-5n-5n-5n-5n)+(7+7+7+7+7+7)#

As you can see, we have 6 of each giving:

#[-(6xx5)xxn ] + [6xx7] = -30n+42#