Algebra Examples

$3 (2 t^{2} - 4 t - 15) + 6 t (5 t + 2)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$3 (2 t^{2}) + 3 (- 4 t) + 3 \cdot - 15 + 6 t (5 t + 2)$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $2$ by $3$ .

$6 t^{2} + 3 (- 4 t) + 3 \cdot - 15 + 6 t (5 t + 2)$

Step 1.2.2

Multiply $- 4$ by $3$ .

$6 t^{2} - 12 t + 3 \cdot - 15 + 6 t (5 t + 2)$

Step 1.2.3

Multiply $3$ by $- 15$ .

$6 t^{2} - 12 t - 45 + 6 t (5 t + 2)$

Step 1.3

Apply the distributive property.

$6 t^{2} - 12 t - 45 + 6 t (5 t) + 6 t \cdot 2$

Step 1.4

Rewrite using the commutative property of multiplication.

$6 t^{2} - 12 t - 45 + 6 \cdot 5 t \cdot t + 6 t \cdot 2$

Step 1.5

Multiply $2$ by $6$ .

$6 t^{2} - 12 t - 45 + 6 \cdot 5 t \cdot t + 12 t$

Step 1.6

Simplify each term.

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Step 1.6.1

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

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Step 1.6.1.1

Move $t$ .

$6 t^{2} - 12 t - 45 + 6 \cdot 5 (t \cdot t) + 12 t$

Step 1.6.1.2

Multiply $t$ by $t$ .

$6 t^{2} - 12 t - 45 + 6 \cdot 5 t^{2} + 12 t$

Step 1.6.2

Multiply $6$ by $5$ .

$6 t^{2} - 12 t - 45 + 30 t^{2} + 12 t$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $6 t^{2} - 12 t - 45 + 30 t^{2} + 12 t$ .

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Step 2.1.1

Add $- 12 t$ and $12 t$ .

$6 t^{2} - 45 + 30 t^{2} + 0$

Step 2.1.2

Add $6 t^{2} - 45 + 30 t^{2}$ and $0$ .

$6 t^{2} - 45 + 30 t^{2}$

Step 2.2

Add $6 t^{2}$ and $30 t^{2}$ .

$36 t^{2} - 45$