How do you find the product #(f+g)(f-g)(f+g)#?

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Answer 1 · 2017-05-31T09:04:11

#f^3+f^2g-fg^2-g^3#

Use expansion to simplify this expression.

Expansion is conventionally done left to right.

Multiply the terms in order as shown with colours.

#(color(red)f+g)(color(red)f-g)(f+g)#

#(color(red)f+g)(f-color(red)g)(f+g)#

#(f+color(red)g)(color(red)f-g)(f+g)#

#(f+color(red)g)(f-color(red)g)(f+g)#

Therefore, #(f+g)(f-g)(f+g)#

#=(f^2-fg+fg-g^2)(f+g)#

#=(f^2-g^2)(f+g)#

Next, follow similar steps as above.

#(color(red)(f^2)-g^2)(color(red)f+g)#

#(color(red)(f^2)-g^2)(f+color(red)g)#

Repeat for #-g^2#.

#=(f^2-g^2)(f+g)#

#color(blue)(=f^3+f^2g-g^2f-g^3)#