Find the Product (x-5)(x+2)(x-6)

$(x - 5) (x + 2) (x - 6)$

Expand $(x - 5) (x + 2)$ using the FOIL Method.

Apply the distributive property.

$(x (x + 2) - 5 (x + 2)) (x - 6)$

Apply the distributive property.

$(x \cdot x + x \cdot 2 - 5 (x + 2)) (x - 6)$

Apply the distributive property.

$(x \cdot x + x \cdot 2 - 5 x - 5 \cdot 2) (x - 6)$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $- 5$ by $2$ .

$(x^{2} + 2 x - 5 x - 10) (x - 6)$

Subtract $5 x$ from $2 x$ .

$(x^{2} - 3 x - 10) (x - 6)$

Expand $(x^{2} - 3 x - 10) (x - 6)$ by multiplying each term in the first expression by each term in the second expression.

$x^{2} x + x^{2} \cdot - 6 - 3 x \cdot x - 3 x \cdot - 6 - 10 x - 10 \cdot - 6$

Simplify terms.

Simplify each term.

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

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

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

$x^{2} x^{1} + x^{2} \cdot - 6 - 3 x \cdot x - 3 x \cdot - 6 - 10 x - 10 \cdot - 6$

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

$x^{2 + 1} + x^{2} \cdot - 6 - 3 x \cdot x - 3 x \cdot - 6 - 10 x - 10 \cdot - 6$

Add $2$ and $1$ .

$x^{3} + x^{2} \cdot - 6 - 3 x \cdot x - 3 x \cdot - 6 - 10 x - 10 \cdot - 6$

Move $- 6$ to the left of $x^{2}$ .

$x^{3} - 6 \cdot x^{2} - 3 x \cdot x - 3 x \cdot - 6 - 10 x - 10 \cdot - 6$

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

Move $x$ .

$x^{3} - 6 x^{2} - 3 (x \cdot x) - 3 x \cdot - 6 - 10 x - 10 \cdot - 6$

Multiply $x$ by $x$ .

$x^{3} - 6 x^{2} - 3 x^{2} - 3 x \cdot - 6 - 10 x - 10 \cdot - 6$

Multiply $- 6$ by $- 3$ .

$x^{3} - 6 x^{2} - 3 x^{2} + 18 x - 10 x - 10 \cdot - 6$

Multiply $- 10$ by $- 6$ .

$x^{3} - 6 x^{2} - 3 x^{2} + 18 x - 10 x + 60$

Simplify by adding terms.

Subtract $3 x^{2}$ from $- 6 x^{2}$ .

$x^{3} - 9 x^{2} + 18 x - 10 x + 60$

Subtract $10 x$ from $18 x$ .

$x^{3} - 9 x^{2} + 8 x + 60$

Find the Product (x-5)(x+2)(x-6)

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