Write in Standard Form (3r+5t)^2

${(3 r + 5 t)}^{2}$

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

Rewrite ${(3 r + 5 t)}^{2}$ as $(3 r + 5 t) (3 r + 5 t)$ .

$(3 r + 5 t) (3 r + 5 t)$

Step 3

Expand $(3 r + 5 t) (3 r + 5 t)$ using the FOIL Method.

Apply the distributive property.

$3 r (3 r + 5 t) + 5 t (3 r + 5 t)$

Apply the distributive property.

$3 r (3 r) + 3 r (5 t) + 5 t (3 r + 5 t)$

Apply the distributive property.

$3 r (3 r) + 3 r (5 t) + 5 t (3 r) + 5 t (5 t)$

Step 4

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 r \cdot r + 3 r (5 t) + 5 t (3 r) + 5 t (5 t)$

Multiply $r$ by $r$ by adding the exponents.

Move $r$ .

$3 \cdot 3 (r \cdot r) + 3 r (5 t) + 5 t (3 r) + 5 t (5 t)$

Multiply $r$ by $r$ .

$3 \cdot 3 r^{2} + 3 r (5 t) + 5 t (3 r) + 5 t (5 t)$

Multiply $3$ by $3$ .

$9 r^{2} + 3 r (5 t) + 5 t (3 r) + 5 t (5 t)$

Rewrite using the commutative property of multiplication.

$9 r^{2} + 3 \cdot 5 r t + 5 t (3 r) + 5 t (5 t)$

Multiply $3$ by $5$ .

$9 r^{2} + 15 r t + 5 t (3 r) + 5 t (5 t)$

Rewrite using the commutative property of multiplication.

$9 r^{2} + 15 r t + 5 \cdot 3 t r + 5 t (5 t)$

Multiply $5$ by $3$ .

$9 r^{2} + 15 r t + 15 t r + 5 t (5 t)$

Rewrite using the commutative property of multiplication.

$9 r^{2} + 15 r t + 15 t r + 5 \cdot 5 t \cdot t$

Multiply $t$ by $t$ by adding the exponents.

Move $t$ .

$9 r^{2} + 15 r t + 15 t r + 5 \cdot 5 (t \cdot t)$

Multiply $t$ by $t$ .

$9 r^{2} + 15 r t + 15 t r + 5 \cdot 5 t^{2}$

Multiply $5$ by $5$ .

$9 r^{2} + 15 r t + 15 t r + 25 t^{2}$

Add $15 r t$ and $15 t r$ .

Move $t$ .

$9 r^{2} + 15 r t + 15 r t + 25 t^{2}$

Add $15 r t$ and $15 r t$ .

$9 r^{2} + 30 r t + 25 t^{2}$

Write in Standard Form (3r+5t)^2

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