Finite Math Examples

$(3 r - 4) (3 r + 3 t)$

Step 1

Expand $(3 r - 4) (3 r + 3 t)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$3 r (3 r + 3 t) - 4 (3 r + 3 t)$

Step 1.2

Apply the distributive property.

$3 r (3 r) + 3 r (3 t) - 4 (3 r + 3 t)$

Step 1.3

Apply the distributive property.

$3 r (3 r) + 3 r (3 t) - 4 (3 r) - 4 (3 t)$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

$3 \cdot 3 r \cdot r + 3 r (3 t) - 4 (3 r) - 4 (3 t)$

Step 2.2

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

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Step 2.2.1

Move $r$ .

$3 \cdot 3 (r \cdot r) + 3 r (3 t) - 4 (3 r) - 4 (3 t)$

Step 2.2.2

Multiply $r$ by $r$ .

$3 \cdot 3 r^{2} + 3 r (3 t) - 4 (3 r) - 4 (3 t)$

Step 2.3

Multiply $3$ by $3$ .

$9 r^{2} + 3 r (3 t) - 4 (3 r) - 4 (3 t)$

Step 2.4

Rewrite using the commutative property of multiplication.

$9 r^{2} + 3 \cdot 3 r t - 4 (3 r) - 4 (3 t)$

Step 2.5

Multiply $3$ by $3$ .

$9 r^{2} + 9 r t - 4 (3 r) - 4 (3 t)$

Step 2.6

Multiply $3$ by $- 4$ .

$9 r^{2} + 9 r t - 12 r - 4 (3 t)$

Step 2.7

Multiply $3$ by $- 4$ .

$9 r^{2} + 9 r t - 12 r - 12 t$