Pre-Algebra Examples

$10 t^{3} - 8 t^{3} + 15 t - 12 = 2 t^{2} (5 t - 4) + (5 t - 4)$

Step 1

Subtract $8 t^{3}$ from $10 t^{3}$ .

$2 t^{3} + 15 t - 12 = 2 t^{2} (5 t - 4) + (5 t - 4)$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$2 t^{3} + 15 t - 12 = 2 t^{2} (5 t) + 2 t^{2} \cdot - 4 + 5 t - 4$

Step 2.2

Rewrite using the commutative property of multiplication.

$2 t^{3} + 15 t - 12 = 2 \cdot 5 t^{2} t + 2 t^{2} \cdot - 4 + 5 t - 4$

Step 2.3

Multiply $- 4$ by $2$ .

$2 t^{3} + 15 t - 12 = 2 \cdot 5 t^{2} t - 8 t^{2} + 5 t - 4$

Step 2.4

Simplify each term.

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Step 2.4.1

Multiply $t^{2}$ by $t$ by adding the exponents.

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Step 2.4.1.1

Move $t$ .

$2 t^{3} + 15 t - 12 = 2 \cdot 5 (t \cdot t^{2}) - 8 t^{2} + 5 t - 4$

Step 2.4.1.2

Multiply $t$ by $t^{2}$ .

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Step 2.4.1.2.1

Raise $t$ to the power of $1$ .

$2 t^{3} + 15 t - 12 = 2 \cdot 5 (t^{1} t^{2}) - 8 t^{2} + 5 t - 4$

Step 2.4.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 t^{3} + 15 t - 12 = 2 \cdot 5 t^{1 + 2} - 8 t^{2} + 5 t - 4$

Step 2.4.1.3

Add $1$ and $2$ .

$2 t^{3} + 15 t - 12 = 2 \cdot 5 t^{3} - 8 t^{2} + 5 t - 4$

Step 2.4.2

Multiply $2$ by $5$ .

$2 t^{3} + 15 t - 12 = 10 t^{3} - 8 t^{2} + 5 t - 4$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$t \approx - 1.0624427, 0.68166411, 1.38077859$

Step 4