Simplify -(a+h)^2+6(a+h)

$- {(a + h)}^{2} + 6 (a + h)$

Rewrite ${(a + h)}^{2}$ as $(a + h) (a + h)$ .

$- ((a + h) (a + h)) + 6 (a + h)$

Expand $(a + h) (a + h)$ using the FOIL Method.

Apply the distributive property.

$- (a (a + h) + h (a + h)) + 6 (a + h)$

Apply the distributive property.

$- (a \cdot a + a h + h (a + h)) + 6 (a + h)$

Apply the distributive property.

$- (a \cdot a + a h + h a + h \cdot h) + 6 (a + h)$

$- (a \cdot a + a h + h a + h \cdot h) + 6 (a + h)$

Simplify and combine like terms.

Simplify each term.

Multiply $a$ by $a$ .

$- (a^{2} + a h + h a + h \cdot h) + 6 (a + h)$

Multiply $h$ by $h$ .

$- (a^{2} + a h + h a + h^{2}) + 6 (a + h)$

$- (a^{2} + a h + h a + h^{2}) + 6 (a + h)$

Add $a h$ and $h a$ .

Reorder $h$ and $a$ .

$- (a^{2} + a h + a h + h^{2}) + 6 (a + h)$

Add $a h$ and $a h$ .

$- (a^{2} + 2 a h + h^{2}) + 6 (a + h)$

$- (a^{2} + 2 a h + h^{2}) + 6 (a + h)$

$- (a^{2} + 2 a h + h^{2}) + 6 (a + h)$

Apply the distributive property.

$- a^{2} - (2 a h) - h^{2} + 6 (a + h)$

Multiply $2$ by $- 1$ .

$- a^{2} - 2 (a h) - h^{2} + 6 (a + h)$

Apply the distributive property.

$- a^{2} - 2 a h - h^{2} + 6 a + 6 h$

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