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

Apr 24, 2016

$- 30 n + 42$

#### Explanation:

Given:$\text{ } 6 \left(- 5 n + 7\right)$

$\textcolor{red}{\text{Shortcut method: Multiply everything inside the brackets by 6}}$

$\textcolor{b l u e}{- 30 n + 42}$

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$\textcolor{red}{\text{Explaining what is really happening.}}$

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

This is exactly the type of thing you have when you write:$\text{ } 6 \left(- 5 n + 7\right)$

This is the same as: $6 \text{ of } \left(- 5 n + 7\right)$

Lets write this out in full:

$\left(- 5 n + 7\right) + \left(- 5 n + 7\right) + \left(- 5 n + 7\right) + \left(- 5 n + 7\right) + \left(- 5 n + 7\right) + \left(- 5 n + 7\right)$

Write this as:

$\left(- 5 n - 5 n - 5 n - 5 n - 5 n - 5 n\right) + \left(7 + 7 + 7 + 7 + 7 + 7\right)$

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

$\left[- \left(6 \times 5\right) \times n\right] + \left[6 \times 7\right] = - 30 n + 42$