Write in Standard Form y=(x+5)(x-1)(x-2)

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

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$y = a x^{2} + b x + c$

Step 2

Expand $(x + 5) (x - 1)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $- 1$ to the left of $x$ .

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

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

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

Multiply $5$ by $- 1$ .

$y = (x^{2} - x + 5 x - 5) (x - 2)$

Add $- x$ and $5 x$ .

$y = (x^{2} + 4 x - 5) (x - 2)$

Step 4

Expand $(x^{2} + 4 x - 5) (x - 2)$ by multiplying each term in the first expression by each term in the second expression.

$y = x^{2} x + x^{2} \cdot - 2 + 4 x \cdot x + 4 x \cdot - 2 - 5 x - 5 \cdot - 2$

Step 5

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 $1$ .

$y = x^{2} x + x^{2} \cdot - 2 + 4 x \cdot x + 4 x \cdot - 2 - 5 x - 5 \cdot - 2$

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

$y = x^{2 + 1} + x^{2} \cdot - 2 + 4 x \cdot x + 4 x \cdot - 2 - 5 x - 5 \cdot - 2$

Add $2$ and $1$ .

$y = x^{3} + x^{2} \cdot - 2 + 4 x \cdot x + 4 x \cdot - 2 - 5 x - 5 \cdot - 2$

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

$y = x^{3} - 2 \cdot x^{2} + 4 x \cdot x + 4 x \cdot - 2 - 5 x - 5 \cdot - 2$

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

Move $x$ .

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

Multiply $x$ by $x$ .

$y = x^{3} - 2 x^{2} + 4 x^{2} + 4 x \cdot - 2 - 5 x - 5 \cdot - 2$

Multiply $- 2$ by $4$ .

$y = x^{3} - 2 x^{2} + 4 x^{2} - 8 x - 5 x - 5 \cdot - 2$

Multiply $- 5$ by $- 2$ .

$y = x^{3} - 2 x^{2} + 4 x^{2} - 8 x - 5 x + 10$

Simplify by adding terms.

Add $- 2 x^{2}$ and $4 x^{2}$ .

$y = x^{3} + 2 x^{2} - 8 x - 5 x + 10$

Subtract $5 x$ from $- 8 x$ .

$y = x^{3} + 2 x^{2} - 13 x + 10$

Step 6

Write in Standard Form y=(x+5)(x-1)(x-2)

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