Simplify (f+g+h)(f+g)

$(f + g + h) (f + g)$

Expand $(f + g + h) (f + g)$ by multiplying each term in the first expression by each term in the second expression.

$f \cdot f + f g + g f + g \cdot g + h f + h g$

Simplify each term.

Multiply $f$ by $f$ .

$f^{2} + f g + g f + g \cdot g + h f + h g$

Multiply $g$ by $g$ .

$f^{2} + f g + g f + g^{2} + h f + h g$

Add $f g$ and $g f$ .

Reorder $g$ and $f$ .

$f^{2} + f g + f g + g^{2} + h f + h g$

Add $f g$ and $f g$ .

$f^{2} + 2 f g + g^{2} + h f + h g$

Reorder $h$ and $f$ .

$f^{2} + 2 f g + g^{2} + f h + h g$

Reorder $h$ and $g$ .

$f^{2} + 2 f g + g^{2} + f h + g h$

Move $g^{2}$ .

$f^{2} + 2 f g + f h + g h + g^{2}$

Move $2 f g$ .

$f^{2} + f h + g h + 2 f g + g^{2}$

Move $f^{2}$ .

$f h + g h + f^{2} + 2 f g + g^{2}$