Algebra Examples

$(x - 1) (x + 2) (X - 3)$

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 $(x - 1) (x + 2)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$(x (x + 2) - 1 (x + 2)) (X - 3)$

Step 2.2

Apply the distributive property.

$(x \cdot x + x \cdot 2 - 1 (x + 2)) (X - 3)$

Step 2.3

Apply the distributive property.

$(x \cdot x + x \cdot 2 - 1 x - 1 \cdot 2) (X - 3)$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $x$ by $x$ .

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

Step 3.1.2

Move $2$ to the left of $x$ .

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

Step 3.1.3

Rewrite $- 1 x$ as $- x$ .

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

Step 3.1.4

Multiply $- 1$ by $2$ .

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

Step 3.2

Subtract $x$ from $2 x$ .

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

Step 4

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

$x^{2} X + x^{2} \cdot - 3 + x X + x \cdot - 3 - 2 X - 2 \cdot - 3$

Step 5

Simplify terms.

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Step 5.1

Simplify each term.

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Step 5.1.1

Move $- 3$ to the left of $x^{2}$ .

$x^{2} X - 3 \cdot x^{2} + x X + x \cdot - 3 - 2 X - 2 \cdot - 3$

Step 5.1.2

Move $- 3$ to the left of $x$ .

$x^{2} X - 3 x^{2} + x X - 3 \cdot x - 2 X - 2 \cdot - 3$

Step 5.1.3

Multiply $- 2$ by $- 3$ .

$x^{2} X - 3 x^{2} + x X - 3 x - 2 X + 6$

Step 5.2

Reorder.

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Step 5.2.1

Move $- 3 x$ .

$x^{2} X - 3 x^{2} + x X - 2 X - 3 x + 6$

Step 5.2.2

Move $- 3 x^{2}$ .

$x^{2} X + x X - 3 x^{2} - 2 X - 3 x + 6$