Expand the Trigonometric Expression (3+a+b)^2

${(3 + a + b)}^{2}$

Step 1

Rewrite ${(3 + a + b)}^{2}$ as $(3 + a + b) (3 + a + b)$ .

$(3 + a + b) (3 + a + b)$

Step 2

Expand $(3 + a + b) (3 + a + b)$ by multiplying each term in the first expression by each term in the second expression.

$3 \cdot 3 + 3 a + 3 b + a \cdot 3 + a \cdot a + a b + b \cdot 3 + b a + b \cdot b$

Step 3

Simplify terms.

Simplify each term.

Multiply $3$ by $3$ .

$9 + 3 a + 3 b + a \cdot 3 + a \cdot a + a b + b \cdot 3 + b a + b \cdot b$

Move $3$ to the left of $a$ .

$9 + 3 a + 3 b + 3 \cdot a + a \cdot a + a b + b \cdot 3 + b a + b \cdot b$

Multiply $a$ by $a$ .

$9 + 3 a + 3 b + 3 a + a^{2} + a b + b \cdot 3 + b a + b \cdot b$

Move $3$ to the left of $b$ .

$9 + 3 a + 3 b + 3 a + a^{2} + a b + 3 \cdot b + b a + b \cdot b$

Multiply $b$ by $b$ .

$9 + 3 a + 3 b + 3 a + a^{2} + a b + 3 b + b a + b^{2}$

Simplify by adding terms.

Add $3 a$ and $3 a$ .

$9 + 6 a + 3 b + a^{2} + a b + 3 b + b a + b^{2}$

Add $3 b$ and $3 b$ .

$9 + 6 a + 6 b + a^{2} + a b + b a + b^{2}$

Step 4

Add $a b$ and $b a$ .

Reorder $b$ and $a$ .

$9 + 6 a + 6 b + a^{2} + a b + a b + b^{2}$

Add $a b$ and $a b$ .

$9 + 6 a + 6 b + a^{2} + 2 a b + b^{2}$