Algebra Examples

$(5 x - 3) (x^{3} - 5 x + 2)$

Step 1

Expand $(5 x - 3) (x^{3} - 5 x + 2)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $x$ by $x^{3}$ by adding the exponents.

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Step 2.1.1.1

Move $x^{3}$ .

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

Step 2.1.1.2

Multiply $x^{3}$ by $x$ .

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Step 2.1.1.2.1

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

$5 (x^{3} x^{1}) + 5 x (- 5 x) + 5 x \cdot 2 - 3 x^{3} - 3 (- 5 x) - 3 \cdot 2$

Step 2.1.1.2.2

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

$5 x^{3 + 1} + 5 x (- 5 x) + 5 x \cdot 2 - 3 x^{3} - 3 (- 5 x) - 3 \cdot 2$

Step 2.1.1.3

Add $3$ and $1$ .

$5 x^{4} + 5 x (- 5 x) + 5 x \cdot 2 - 3 x^{3} - 3 (- 5 x) - 3 \cdot 2$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$5 x^{4} + 5 \cdot - 5 x \cdot x + 5 x \cdot 2 - 3 x^{3} - 3 (- 5 x) - 3 \cdot 2$

Step 2.1.3

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

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Step 2.1.3.1

Move $x$ .

$5 x^{4} + 5 \cdot - 5 (x \cdot x) + 5 x \cdot 2 - 3 x^{3} - 3 (- 5 x) - 3 \cdot 2$

Step 2.1.3.2

Multiply $x$ by $x$ .

$5 x^{4} + 5 \cdot - 5 x^{2} + 5 x \cdot 2 - 3 x^{3} - 3 (- 5 x) - 3 \cdot 2$

Step 2.1.4

Multiply $5$ by $- 5$ .

$5 x^{4} - 25 x^{2} + 5 x \cdot 2 - 3 x^{3} - 3 (- 5 x) - 3 \cdot 2$

Step 2.1.5

Multiply $2$ by $5$ .

$5 x^{4} - 25 x^{2} + 10 x - 3 x^{3} - 3 (- 5 x) - 3 \cdot 2$

Step 2.1.6

Multiply $- 5$ by $- 3$ .

$5 x^{4} - 25 x^{2} + 10 x - 3 x^{3} + 15 x - 3 \cdot 2$

Step 2.1.7

Multiply $- 3$ by $2$ .

$5 x^{4} - 25 x^{2} + 10 x - 3 x^{3} + 15 x - 6$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $10 x$ and $15 x$ .

$5 x^{4} - 25 x^{2} - 3 x^{3} + 25 x - 6$

Step 2.2.2

Move $- 25 x^{2}$ .

$5 x^{4} - 3 x^{3} - 25 x^{2} + 25 x - 6$