What is expand (l-|x|)cos((npix)/l) ?

The solution to expand (l-|x|)cos((npix)/l) is lcos((pinx)/l)-cos((pinx)/l)|x|

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expand (l-|x|)cos((npix)/l)

expand

(l - ∣ x ∣) cos (\frac{nπ x}{l})

l cos (\frac{πn x}{l}) - cos (\frac{πn x}{l}) ∣ x ∣

Solution steps

(l - ∣ x ∣) cos (\frac{nπ x}{l})

= cos (\frac{πn x}{l}) (l - ∣ x ∣)

Apply the distributive law:

a (b - c) = ab - a c

a = cos (\frac{nπ x}{l}), b = l, c = ∣ x ∣

= cos (\frac{nπ x}{l}) l - cos (\frac{nπ x}{l}) ∣ x ∣

= l cos (\frac{πn x}{l}) - cos (\frac{πn x}{l}) ∣ x ∣

\frac{4 ( s + 2 )}{s ( s ^{3} + 2 s ^{2} + 3 s + 4 )}

(\frac{( k s - s ) ( k ^{2} - 1 ) ( s - 1 )}{s ^{2} - s - 2}) + (k - 1)

\frac{x ^{2}}{( 1 + 0.6 x ) ( 1 - x )}

\frac{( 1 + 2 x ) ^{4}}{8}

(- 16 e^{x} sin (x)) (8 e^{x} cos (x) - 8 e^{x} sin (x))

What is expand (l-|x|)cos((npix)/l) ?
The solution to expand (l-|x|)cos((npix)/l) is lcos((pinx)/l)-cos((pinx)/l)|x|