How do you simplify $- 6 (7 + x)$ $-6(7 + x)$ ?

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Answer 1 · 2016-05-07T20:59:15

$- 42 - 6 x$ $-42-6x$

$Detailed explanation building up to the shortcut method$ $color(blue)("Detailed explanation building up to the shortcut method")$

When it is written in the form $- 6 (7 + x)$ $-6(7+x)$ it is the same as $(- 6) \times (7 + x)$ $(-6)xx(7+x)$

I will deal with the negative aspect of this in a while.

This means that you have 6 lots of $(7 + x)$ $(7+x)$

So you have 6 lots of 7 and $6 \times 7 = 42$ $6xx7=42$

You also have 6 lots of x and $6 \times x = 6 x$ $6xx x =6x$

So, ignoring the negative part of -6,

$6 (7 + x) = 42 + 6 x$ $6(7+x)=42+6x$

$Everything inside the bracket is multiplied by 6$ $color(brown)("Everything inside the bracket is multiplied by 6")$

$However, we have - 6 (7 + x)$ $color(brown)("However, we have "-6(7+x))$

This is the same as $(- 1) \times 6 \times (7 + x)$ $(-1)xx6xx(7+x)$

Multiply everything inside the bracket by $(- 1)$ $(-1)$ giving:

$6 \times (- 7 - x)$ $6xx(-7-x)$

Now multiply everything inside the bracket by 6 giving:

$- 42 - 6 x$ $-42-6x$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Shortcut method$ $color(blue)("Shortcut method")$

Given: $- 6 (7 + x)$ $-6(7+x)$

$Multiply everything inside the bracket by -6$ $color(brown)("Multiply everything inside the bracket by -6")$

$- 42 - 6 x$ $-42-6x$

How do you simplify −6(7+x)-6(7 + x)?