Simplify 2(a+h)^2

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

Step 1

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

$2 ((a + h) (a + h))$

Step 2

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

Apply the distributive property.

$2 (a (a + h) + h (a + h))$

Apply the distributive property.

$2 (a \cdot a + a h + h (a + h))$

Apply the distributive property.

$2 (a \cdot a + a h + h a + h \cdot h)$

$2 (a \cdot a + a h + h a + h \cdot h)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $a$ by $a$ .

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

Multiply $h$ by $h$ .

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

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

Add $a h$ and $h a$ .

Reorder $h$ and $a$ .

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

Add $a h$ and $a h$ .

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

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

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

Step 4

Apply the distributive property.

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

Step 5

Multiply $2$ by $2$ .

$2 a^{2} + 4 a h + 2 h^{2}$

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