Evaluate (4x^5+11)^2

${(4 x^{5} + 11)}^{2}$

Step 1

Rewrite ${(4 x^{5} + 11)}^{2}$ as $(4 x^{5} + 11) (4 x^{5} + 11)$ .

$(4 x^{5} + 11) (4 x^{5} + 11)$

Step 2

Expand $(4 x^{5} + 11) (4 x^{5} + 11)$ using the FOIL Method.

Apply the distributive property.

$4 x^{5} (4 x^{5} + 11) + 11 (4 x^{5} + 11)$

Apply the distributive property.

$4 x^{5} (4 x^{5}) + 4 x^{5} \cdot 11 + 11 (4 x^{5} + 11)$

Apply the distributive property.

$4 x^{5} (4 x^{5}) + 4 x^{5} \cdot 11 + 11 (4 x^{5}) + 11 \cdot 11$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 x^{5} x^{5} + 4 x^{5} \cdot 11 + 11 (4 x^{5}) + 11 \cdot 11$

Multiply $x^{5}$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

$4 \cdot 4 (x^{5} x^{5}) + 4 x^{5} \cdot 11 + 11 (4 x^{5}) + 11 \cdot 11$

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

$4 \cdot 4 x^{5 + 5} + 4 x^{5} \cdot 11 + 11 (4 x^{5}) + 11 \cdot 11$

Add $5$ and $5$ .

$4 \cdot 4 x^{10} + 4 x^{5} \cdot 11 + 11 (4 x^{5}) + 11 \cdot 11$

Multiply $4$ by $4$ .

$16 x^{10} + 4 x^{5} \cdot 11 + 11 (4 x^{5}) + 11 \cdot 11$

Multiply $11$ by $4$ .

$16 x^{10} + 44 x^{5} + 11 (4 x^{5}) + 11 \cdot 11$

Multiply $4$ by $11$ .

$16 x^{10} + 44 x^{5} + 44 x^{5} + 11 \cdot 11$

Multiply $11$ by $11$ .

$16 x^{10} + 44 x^{5} + 44 x^{5} + 121$

Add $44 x^{5}$ and $44 x^{5}$ .

$16 x^{10} + 88 x^{5} + 121$