# Multiply (n-5) (n+5). Help with steps please?

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( n - 5 ) ( n + 5 ) = n² + 5n - 5n - 25 = n² - 25

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• Use FOIL

(n - 5)(n + 5)

F(First ; n X n = n^2

O(Outside) ; n X 5 = 5n

I(Inside) : -5 X n = -5n

L(Last) ; - 5 X +5 = -25

Collect like terms

n^2 + 5n - 5n - 25 = n^2 - 25

Sone!!!!!

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• (n - 5)(n + 5)

= n^2 - 5n + 5n - 25

= n^2 - 25

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• Use the FOIL method to work out the answer as n^2 -25

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• (n - 5)(n + 5) = n^2 - 25

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• Difference of squares

n² - 25

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• You can use distribution or FOIL:

Distribution:

n(n + 5) - 5(n + 5)

= n² + 5n - 5n - 25

= n² - 25

FOIL:

First: n * n --> n²

Outer: n * 5 --> 5n

Inner: -5 * n --> -5n

Last: 5 * -5 --> -25

Add those up; you can cancel 5n and -5n

= n² - 25

Now that you've seen it the long way, you can just recognize the pattern. It's known as a difference of squares factoring:

a² - b² = (a + b)(a - b)

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