Algebra Examples

$9 x (3 + 5 x)$

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

Simplify by multiplying through.

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Step 2.1

Apply the distributive property.

$9 x \cdot 3 + 9 x (5 x)$

Step 2.2

Simplify the expression.

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Step 2.2.1

Multiply $3$ by $9$ .

$27 x + 9 x (5 x)$

Step 2.2.2

Rewrite using the commutative property of multiplication.

$27 x + 9 \cdot 5 x \cdot x$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $x$ .

$27 x + 9 \cdot 5 (x \cdot x)$

Step 3.1.2

Multiply $x$ by $x$ .

$27 x + 9 \cdot 5 x^{2}$

Step 3.2

Multiply $9$ by $5$ .

$27 x + 45 x^{2}$

Step 4

Reorder $27 x$ and $45 x^{2}$ .

$45 x^{2} + 27 x$