Write in Standard Form y=x(x+3)(x-3)

$y = x (x + 3) (x - 3)$

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

Simplify by multiplying through.

Apply the distributive property.

$y = (x \cdot x + x \cdot 3) (x - 3)$

Simplify the expression.

Multiply $x$ by $x$ .

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

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

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

Step 3

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

Apply the distributive property.

$y = x^{2} (x - 3) + 3 x (x - 3)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 4

Simplify and combine like terms.

Simplify each term.

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

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

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

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

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

$y = x^{2 + 1} + x^{2} \cdot - 3 + 3 x \cdot x + 3 x \cdot - 3$

Add $2$ and $1$ .

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

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

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 3$ by $3$ .

$y = x^{3} - 3 x^{2} + 3 x^{2} - 9 x$

Add $- 3 x^{2}$ and $3 x^{2}$ .

$y = x^{3} + 0 - 9 x$

Add $x^{3}$ and $0$ .

$y = x^{3} - 9 x$

Step 5

Write in Standard Form y=x(x+3)(x-3)

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