Algebra Examples

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

Step 1

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

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

Step 2

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

Tap for more steps...

Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Rewrite using the commutative property of multiplication.

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

Step 3.1.2

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

Tap for more steps...

Step 3.1.2.1

Move $r$ .

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

Step 3.1.2.2

Multiply $r$ by $r$ .

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

Step 3.1.3

Multiply $3$ by $3$ .

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

Step 3.1.4

Rewrite using the commutative property of multiplication.

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

Step 3.1.5

Multiply $3$ by $5$ .

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

Step 3.1.6

Rewrite using the commutative property of multiplication.

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

Step 3.1.7

Multiply $5$ by $3$ .

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

Step 3.1.8

Rewrite using the commutative property of multiplication.

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

Step 3.1.9

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

Tap for more steps...

Step 3.1.9.1

Move $t$ .

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

Step 3.1.9.2

Multiply $t$ by $t$ .

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

Step 3.1.10

Multiply $5$ by $5$ .

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

Step 3.2

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

Tap for more steps...

Step 3.2.1

Move $t$ .

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

Step 3.2.2

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

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