Simplify (a+b)^2

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

Step 1

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

$(a + b) (a + b)$

Step 2

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

Apply the distributive property.

$a (a + b) + b (a + b)$

Apply the distributive property.

$a \cdot a + a b + b (a + b)$

Apply the distributive property.

$a \cdot a + a b + b a + b \cdot b$

$a \cdot a + a b + b a + b \cdot b$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $a$ by $a$ .

$a^{2} + a b + b a + b \cdot b$

Multiply $b$ by $b$ .

$a^{2} + a b + b a + b^{2}$

$a^{2} + a b + b a + b^{2}$

Add $a b$ and $b a$ .

Reorder $b$ and $a$ .

$a^{2} + a b + a b + b^{2}$

Add $a b$ and $a b$ .

$a^{2} + 2 a b + b^{2}$

$a^{2} + 2 a b + b^{2}$

$a^{2} + 2 a b + b^{2}$

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