Basic Math Examples

$- 4 (3 t - 3) (3 t - 3) + 9 (t + 1)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$(- 4 (3 t) - 4 \cdot - 3) (3 t - 3) + 9 (t + 1)$

Step 1.2

Multiply $3$ by $- 4$ .

$(- 12 t - 4 \cdot - 3) (3 t - 3) + 9 (t + 1)$

Step 1.3

Multiply $- 4$ by $- 3$ .

$(- 12 t + 12) (3 t - 3) + 9 (t + 1)$

Step 1.4

Expand $(- 12 t + 12) (3 t - 3)$ using the FOIL Method.

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Step 1.4.1

Apply the distributive property.

$- 12 t (3 t - 3) + 12 (3 t - 3) + 9 (t + 1)$

Step 1.4.2

Apply the distributive property.

$- 12 t (3 t) - 12 t \cdot - 3 + 12 (3 t - 3) + 9 (t + 1)$

Step 1.4.3

Apply the distributive property.

$- 12 t (3 t) - 12 t \cdot - 3 + 12 (3 t) + 12 \cdot - 3 + 9 (t + 1)$

Step 1.5

Simplify and combine like terms.

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Step 1.5.1

Simplify each term.

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Step 1.5.1.1

Rewrite using the commutative property of multiplication.

$- 12 \cdot 3 t \cdot t - 12 t \cdot - 3 + 12 (3 t) + 12 \cdot - 3 + 9 (t + 1)$

Step 1.5.1.2

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

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Step 1.5.1.2.1

Move $t$ .

$- 12 \cdot 3 (t \cdot t) - 12 t \cdot - 3 + 12 (3 t) + 12 \cdot - 3 + 9 (t + 1)$

Step 1.5.1.2.2

Multiply $t$ by $t$ .

$- 12 \cdot 3 t^{2} - 12 t \cdot - 3 + 12 (3 t) + 12 \cdot - 3 + 9 (t + 1)$

Step 1.5.1.3

Multiply $- 12$ by $3$ .

$- 36 t^{2} - 12 t \cdot - 3 + 12 (3 t) + 12 \cdot - 3 + 9 (t + 1)$

Step 1.5.1.4

Multiply $- 3$ by $- 12$ .

$- 36 t^{2} + 36 t + 12 (3 t) + 12 \cdot - 3 + 9 (t + 1)$

Step 1.5.1.5

Multiply $3$ by $12$ .

$- 36 t^{2} + 36 t + 36 t + 12 \cdot - 3 + 9 (t + 1)$

Step 1.5.1.6

Multiply $12$ by $- 3$ .

$- 36 t^{2} + 36 t + 36 t - 36 + 9 (t + 1)$

Step 1.5.2

Add $36 t$ and $36 t$ .

$- 36 t^{2} + 72 t - 36 + 9 (t + 1)$

Step 1.6

Apply the distributive property.

$- 36 t^{2} + 72 t - 36 + 9 t + 9 \cdot 1$

Step 1.7

Multiply $9$ by $1$ .

$- 36 t^{2} + 72 t - 36 + 9 t + 9$

Step 2

Simplify by adding terms.

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Step 2.1

Add $72 t$ and $9 t$ .

$- 36 t^{2} + 81 t - 36 + 9$

Step 2.2

Add $- 36$ and $9$ .

$- 36 t^{2} + 81 t - 27$