Simplify (x-2)(x+3)(x-5)

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

Expand $(x - 2) (x + 3)$ using the FOIL Method.

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Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

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Simplify each term.

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Multiply $x$ by $x$ .

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

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

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

Multiply $- 2$ by $3$ .

$(x^{2} + 3 x - 2 x - 6) (x - 5)$

Subtract $2 x$ from $3 x$ .

$(x^{2} + x - 6) (x - 5)$

Expand $(x^{2} + x - 6) (x - 5)$ by multiplying each term in the first expression by each term in the second expression.

$x^{2} x + x^{2} \cdot - 5 + x \cdot x + x \cdot - 5 - 6 x - 6 \cdot - 5$

Simplify terms.

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Simplify each term.

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

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

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

$x^{2} x^{1} + x^{2} \cdot - 5 + x \cdot x + x \cdot - 5 - 6 x - 6 \cdot - 5$

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

$x^{2 + 1} + x^{2} \cdot - 5 + x \cdot x + x \cdot - 5 - 6 x - 6 \cdot - 5$

Add $2$ and $1$ .

$x^{3} + x^{2} \cdot - 5 + x \cdot x + x \cdot - 5 - 6 x - 6 \cdot - 5$

Move $- 5$ to the left of $x^{2}$ .

$x^{3} - 5 \cdot x^{2} + x \cdot x + x \cdot - 5 - 6 x - 6 \cdot - 5$

Multiply $x$ by $x$ .

$x^{3} - 5 x^{2} + x^{2} + x \cdot - 5 - 6 x - 6 \cdot - 5$

Move $- 5$ to the left of $x$ .

$x^{3} - 5 x^{2} + x^{2} - 5 \cdot x - 6 x - 6 \cdot - 5$

Multiply $- 6$ by $- 5$ .

$x^{3} - 5 x^{2} + x^{2} - 5 x - 6 x + 30$

Simplify by adding terms.

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Add $- 5 x^{2}$ and $x^{2}$ .

$x^{3} - 4 x^{2} - 5 x - 6 x + 30$

Subtract $6 x$ from $- 5 x$ .

$x^{3} - 4 x^{2} - 11 x + 30$

Simplify (x-2)(x+3)(x-5)

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