Expand the Trigonometric Expression (6a^2+2)^2

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

Step 1

Rewrite ${(6 a^{2} + 2)}^{2}$ as $(6 a^{2} + 2) (6 a^{2} + 2)$ .

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

Step 2

Expand $(6 a^{2} + 2) (6 a^{2} + 2)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $a^{2}$ by $a^{2}$ by adding the exponents.

Move $a^{2}$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $2$ and $2$ .

$6 \cdot 6 a^{4} + 6 a^{2} \cdot 2 + 2 (6 a^{2}) + 2 \cdot 2$

Multiply $6$ by $6$ .

$36 a^{4} + 6 a^{2} \cdot 2 + 2 (6 a^{2}) + 2 \cdot 2$

Multiply $2$ by $6$ .

$36 a^{4} + 12 a^{2} + 2 (6 a^{2}) + 2 \cdot 2$

Multiply $6$ by $2$ .

$36 a^{4} + 12 a^{2} + 12 a^{2} + 2 \cdot 2$

Multiply $2$ by $2$ .

$36 a^{4} + 12 a^{2} + 12 a^{2} + 4$

Add $12 a^{2}$ and $12 a^{2}$ .

$36 a^{4} + 24 a^{2} + 4$