Evaluate (p+q)^2

${(p + q)}^{2}$

Rewrite ${(p + q)}^{2}$ as $(p + q) (p + q)$ .

$(p + q) (p + q)$

Expand $(p + q) (p + q)$ using the FOIL Method.

Apply the distributive property.

$p (p + q) + q (p + q)$

Apply the distributive property.

$p \cdot p + p q + q (p + q)$

Apply the distributive property.

$p \cdot p + p q + q p + q \cdot q$

$p \cdot p + p q + q p + q \cdot q$

Simplify and combine like terms.

Simplify each term.

Multiply $p$ by $p$ .

$p^{2} + p q + q p + q \cdot q$

Multiply $q$ by $q$ .

$p^{2} + p q + q p + q^{2}$

$p^{2} + p q + q p + q^{2}$

Add $p q$ and $q p$ .

Reorder $q$ and $p$ .

$p^{2} + p q + p q + q^{2}$

Add $p q$ and $p q$ .

$p^{2} + 2 p q + q^{2}$

$p^{2} + 2 p q + q^{2}$

$p^{2} + 2 p q + q^{2}$

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