Algebra Examples

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

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

Expand $(x - 5) (x + 5)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

$(x \cdot x + x \cdot 5 - 5 (x + 5)) (2 x - 1)$

Step 2.3

Apply the distributive property.

$(x \cdot x + x \cdot 5 - 5 x - 5 \cdot 5) (2 x - 1)$

Step 3

Simplify terms.

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Step 3.1

Combine the opposite terms in $x \cdot x + x \cdot 5 - 5 x - 5 \cdot 5$ .

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Step 3.1.1

Reorder the factors in the terms $x \cdot 5$ and $- 5 x$ .

$(x \cdot x + 5 x - 5 x - 5 \cdot 5) (2 x - 1)$

Step 3.1.2

Subtract $5 x$ from $5 x$ .

$(x \cdot x + 0 - 5 \cdot 5) (2 x - 1)$

Step 3.1.3

Add $x \cdot x$ and $0$ .

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

Step 3.2

Simplify each term.

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Step 3.2.1

Multiply $x$ by $x$ .

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

Step 3.2.2

Multiply $- 5$ by $5$ .

$(x^{2} - 25) (2 x - 1)$

Step 4

Expand $(x^{2} - 25) (2 x - 1)$ using the FOIL Method.

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Step 4.1

Apply the distributive property.

$x^{2} (2 x - 1) - 25 (2 x - 1)$

Step 4.2

Apply the distributive property.

$x^{2} (2 x) + x^{2} \cdot - 1 - 25 (2 x - 1)$

Step 4.3

Apply the distributive property.

$x^{2} (2 x) + x^{2} \cdot - 1 - 25 (2 x) - 25 \cdot - 1$

Step 5

Simplify each term.

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Step 5.1

Rewrite using the commutative property of multiplication.

$2 x^{2} x + x^{2} \cdot - 1 - 25 (2 x) - 25 \cdot - 1$

Step 5.2

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

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Step 5.2.1

Move $x$ .

$2 (x \cdot x^{2}) + x^{2} \cdot - 1 - 25 (2 x) - 25 \cdot - 1$

Step 5.2.2

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

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Step 5.2.2.1

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

$2 (x^{1} x^{2}) + x^{2} \cdot - 1 - 25 (2 x) - 25 \cdot - 1$

Step 5.2.2.2

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

$2 x^{1 + 2} + x^{2} \cdot - 1 - 25 (2 x) - 25 \cdot - 1$

Step 5.2.3

Add $1$ and $2$ .

$2 x^{3} + x^{2} \cdot - 1 - 25 (2 x) - 25 \cdot - 1$

Step 5.3

Move $- 1$ to the left of $x^{2}$ .

$2 x^{3} - 1 \cdot x^{2} - 25 (2 x) - 25 \cdot - 1$

Step 5.4

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

$2 x^{3} - x^{2} - 25 (2 x) - 25 \cdot - 1$

Step 5.5

Multiply $2$ by $- 25$ .

$2 x^{3} - x^{2} - 50 x - 25 \cdot - 1$

Step 5.6

Multiply $- 25$ by $- 1$ .

$2 x^{3} - x^{2} - 50 x + 25$