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

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Answer 1 · 2016-04-24T15:24:43

$- 30 n + 42$ $-30n+42$

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

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

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

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$Explaining what is really happening.$ $color(red)("Explaining what is really happening.")$

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

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

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

Lets write this out in full:

$(- 5 n + 7) + (- 5 n + 7) + (- 5 n + 7) + (- 5 n + 7) + (- 5 n + 7) + (- 5 n + 7)$ $(-5n+7)+(-5n+7)+(-5n+7)+(-5n+7)+(-5n+7)+(-5n+7)$

Write this as:

$(- 5 n - 5 n - 5 n - 5 n - 5 n - 5 n) + (7 + 7 + 7 + 7 + 7 + 7)$ $(-5n-5n-5n-5n-5n-5n)+(7+7+7+7+7+7)$

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

$[- (6 \times 5) \times n] + [6 \times 7] = - 30 n + 42$ $[-(6xx5)xxn ] + [6xx7] = -30n+42$

How do you simplify 6(−5n+7)6(-5n+7)?