Algebra Examples

$- 3 x (5 x + 1) (8 - 2 x)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Simplify terms.

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Step 2.1

Apply the distributive property.

$(- 3 x (5 x) - 3 x \cdot 1) (8 - 2 x)$

Step 2.2

Simplify the expression.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$(- 3 \cdot 5 x \cdot x - 3 x \cdot 1) (8 - 2 x)$

Step 2.2.2

Multiply $- 3$ by $1$ .

$(- 3 \cdot 5 x \cdot x - 3 x) (8 - 2 x)$

Step 2.3

Simplify each term.

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Step 2.3.1

Multiply $x$ by $x$ by adding the exponents.

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Step 2.3.1.1

Move $x$ .

$(- 3 \cdot 5 (x \cdot x) - 3 x) (8 - 2 x)$

Step 2.3.1.2

Multiply $x$ by $x$ .

$(- 3 \cdot 5 x^{2} - 3 x) (8 - 2 x)$

Step 2.3.2

Multiply $- 3$ by $5$ .

$(- 15 x^{2} - 3 x) (8 - 2 x)$

Step 3

Expand $(- 15 x^{2} - 3 x) (8 - 2 x)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$- 15 x^{2} (8 - 2 x) - 3 x (8 - 2 x)$

Step 3.2

Apply the distributive property.

$- 15 x^{2} \cdot 8 - 15 x^{2} (- 2 x) - 3 x (8 - 2 x)$

Step 3.3

Apply the distributive property.

$- 15 x^{2} \cdot 8 - 15 x^{2} (- 2 x) - 3 x \cdot 8 - 3 x (- 2 x)$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $8$ by $- 15$ .

$- 120 x^{2} - 15 x^{2} (- 2 x) - 3 x \cdot 8 - 3 x (- 2 x)$

Step 4.1.2

Rewrite using the commutative property of multiplication.

$- 120 x^{2} - 15 \cdot - 2 x^{2} x - 3 x \cdot 8 - 3 x (- 2 x)$

Step 4.1.3

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

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Step 4.1.3.1

Move $x$ .

$- 120 x^{2} - 15 \cdot - 2 (x \cdot x^{2}) - 3 x \cdot 8 - 3 x (- 2 x)$

Step 4.1.3.2

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

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Step 4.1.3.2.1

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

$- 120 x^{2} - 15 \cdot - 2 (x^{1} x^{2}) - 3 x \cdot 8 - 3 x (- 2 x)$

Step 4.1.3.2.2

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

$- 120 x^{2} - 15 \cdot - 2 x^{1 + 2} - 3 x \cdot 8 - 3 x (- 2 x)$

Step 4.1.3.3

Add $1$ and $2$ .

$- 120 x^{2} - 15 \cdot - 2 x^{3} - 3 x \cdot 8 - 3 x (- 2 x)$

Step 4.1.4

Multiply $- 15$ by $- 2$ .

$- 120 x^{2} + 30 x^{3} - 3 x \cdot 8 - 3 x (- 2 x)$

Step 4.1.5

Multiply $8$ by $- 3$ .

$- 120 x^{2} + 30 x^{3} - 24 x - 3 x (- 2 x)$

Step 4.1.6

Rewrite using the commutative property of multiplication.

$- 120 x^{2} + 30 x^{3} - 24 x - 3 \cdot - 2 x \cdot x$

Step 4.1.7

Multiply $x$ by $x$ by adding the exponents.

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Step 4.1.7.1

Move $x$ .

$- 120 x^{2} + 30 x^{3} - 24 x - 3 \cdot - 2 (x \cdot x)$

Step 4.1.7.2

Multiply $x$ by $x$ .

$- 120 x^{2} + 30 x^{3} - 24 x - 3 \cdot - 2 x^{2}$

Step 4.1.8

Multiply $- 3$ by $- 2$ .

$- 120 x^{2} + 30 x^{3} - 24 x + 6 x^{2}$

Step 4.2

Add $- 120 x^{2}$ and $6 x^{2}$ .

$- 114 x^{2} + 30 x^{3} - 24 x$

Step 5

Reorder $- 114 x^{2}$ and $30 x^{3}$ .

$30 x^{3} - 114 x^{2} - 24 x$