Finite Math Examples

$4 (x^{3} + 2 x^{2} - 7 x + 8) - 3 (8 x^{3} - 2 x^{2} + 8 x + 11)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$4 x^{3} + 4 (2 x^{2}) + 4 (- 7 x) + 4 \cdot 8 - 3 (8 x^{3} - 2 x^{2} + 8 x + 11)$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $2$ by $4$ .

$4 x^{3} + 8 x^{2} + 4 (- 7 x) + 4 \cdot 8 - 3 (8 x^{3} - 2 x^{2} + 8 x + 11)$

Step 1.2.2

Multiply $- 7$ by $4$ .

$4 x^{3} + 8 x^{2} - 28 x + 4 \cdot 8 - 3 (8 x^{3} - 2 x^{2} + 8 x + 11)$

Step 1.2.3

Multiply $4$ by $8$ .

$4 x^{3} + 8 x^{2} - 28 x + 32 - 3 (8 x^{3} - 2 x^{2} + 8 x + 11)$

Step 1.3

Apply the distributive property.

$4 x^{3} + 8 x^{2} - 28 x + 32 - 3 (8 x^{3}) - 3 (- 2 x^{2}) - 3 (8 x) - 3 \cdot 11$

Step 1.4

Simplify.

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Step 1.4.1

Multiply $8$ by $- 3$ .

$4 x^{3} + 8 x^{2} - 28 x + 32 - 24 x^{3} - 3 (- 2 x^{2}) - 3 (8 x) - 3 \cdot 11$

Step 1.4.2

Multiply $- 2$ by $- 3$ .

$4 x^{3} + 8 x^{2} - 28 x + 32 - 24 x^{3} + 6 x^{2} - 3 (8 x) - 3 \cdot 11$

Step 1.4.3

Multiply $8$ by $- 3$ .

$4 x^{3} + 8 x^{2} - 28 x + 32 - 24 x^{3} + 6 x^{2} - 24 x - 3 \cdot 11$

Step 1.4.4

Multiply $- 3$ by $11$ .

$4 x^{3} + 8 x^{2} - 28 x + 32 - 24 x^{3} + 6 x^{2} - 24 x - 33$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $24 x^{3}$ from $4 x^{3}$ .

$- 20 x^{3} + 8 x^{2} - 28 x + 32 + 6 x^{2} - 24 x - 33$

Step 2.2

Add $8 x^{2}$ and $6 x^{2}$ .

$- 20 x^{3} + 14 x^{2} - 28 x + 32 - 24 x - 33$

Step 2.3

Subtract $24 x$ from $- 28 x$ .

$- 20 x^{3} + 14 x^{2} - 52 x + 32 - 33$

Step 2.4

Subtract $33$ from $32$ .

$- 20 x^{3} + 14 x^{2} - 52 x - 1$