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

Question

1969 views around the world

You can reuse this answer
Creative Commons License

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 $-g^2$ .

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

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

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