Find the Degree f(x)=(3x^4+1)^2

$f (x) = {(3 x^{4} + 1)}^{2}$

Step 1

Simplify and reorder the polynomial.

Rewrite ${(3 x^{4} + 1)}^{2}$ as $(3 x^{4} + 1) (3 x^{4} + 1)$ .

$(3 x^{4} + 1) (3 x^{4} + 1)$

Expand $(3 x^{4} + 1) (3 x^{4} + 1)$ using the FOIL Method.

Apply the distributive property.

$3 x^{4} (3 x^{4} + 1) + 1 (3 x^{4} + 1)$

Apply the distributive property.

$3 x^{4} (3 x^{4}) + 3 x^{4} \cdot 1 + 1 (3 x^{4} + 1)$

Apply the distributive property.

$3 x^{4} (3 x^{4}) + 3 x^{4} \cdot 1 + 1 (3 x^{4}) + 1 \cdot 1$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 x^{4} x^{4} + 3 x^{4} \cdot 1 + 1 (3 x^{4}) + 1 \cdot 1$

Multiply $x^{4}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$3 \cdot 3 (x^{4} x^{4}) + 3 x^{4} \cdot 1 + 1 (3 x^{4}) + 1 \cdot 1$

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

$3 \cdot 3 x^{4 + 4} + 3 x^{4} \cdot 1 + 1 (3 x^{4}) + 1 \cdot 1$

Add $4$ and $4$ .

$3 \cdot 3 x^{8} + 3 x^{4} \cdot 1 + 1 (3 x^{4}) + 1 \cdot 1$

Multiply $3$ by $3$ .

$9 x^{8} + 3 x^{4} \cdot 1 + 1 (3 x^{4}) + 1 \cdot 1$

Multiply $3$ by $1$ .

$9 x^{8} + 3 x^{4} + 1 (3 x^{4}) + 1 \cdot 1$

Multiply $3 x^{4}$ by $1$ .

$9 x^{8} + 3 x^{4} + 3 x^{4} + 1 \cdot 1$

Multiply $1$ by $1$ .

$9 x^{8} + 3 x^{4} + 3 x^{4} + 1$

Add $3 x^{4}$ and $3 x^{4}$ .

$9 x^{8} + 6 x^{4} + 1$

Step 2

The largest exponent is the degree of the polynomial.

$8$