Write in Standard Form (5r^2+4)(5r^2+4)

$(5 r^{2} + 4) (5 r^{2} + 4)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Expand $(5 r^{2} + 4) (5 r^{2} + 4)$ using the FOIL Method.

Apply the distributive property.

$5 r^{2} (5 r^{2} + 4) + 4 (5 r^{2} + 4)$

Apply the distributive property.

$5 r^{2} (5 r^{2}) + 5 r^{2} \cdot 4 + 4 (5 r^{2} + 4)$

Apply the distributive property.

$5 r^{2} (5 r^{2}) + 5 r^{2} \cdot 4 + 4 (5 r^{2}) + 4 \cdot 4$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 5 r^{2} r^{2} + 5 r^{2} \cdot 4 + 4 (5 r^{2}) + 4 \cdot 4$

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

Move $r^{2}$ .

$5 \cdot 5 (r^{2} r^{2}) + 5 r^{2} \cdot 4 + 4 (5 r^{2}) + 4 \cdot 4$

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

$5 \cdot 5 r^{2 + 2} + 5 r^{2} \cdot 4 + 4 (5 r^{2}) + 4 \cdot 4$

Add $2$ and $2$ .

$5 \cdot 5 r^{4} + 5 r^{2} \cdot 4 + 4 (5 r^{2}) + 4 \cdot 4$

Multiply $5$ by $5$ .

$25 r^{4} + 5 r^{2} \cdot 4 + 4 (5 r^{2}) + 4 \cdot 4$

Multiply $4$ by $5$ .

$25 r^{4} + 20 r^{2} + 4 (5 r^{2}) + 4 \cdot 4$

Multiply $5$ by $4$ .

$25 r^{4} + 20 r^{2} + 20 r^{2} + 4 \cdot 4$

Multiply $4$ by $4$ .

$25 r^{4} + 20 r^{2} + 20 r^{2} + 16$

Add $20 r^{2}$ and $20 r^{2}$ .

$25 r^{4} + 40 r^{2} + 16$