Algebra Examples

$(x + 1) (x^{2} + 3 x + 2)$

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

Expand $(x + 1) (x^{2} + 3 x + 2)$ by multiplying each term in the first expression by each term in the second expression.

$x \cdot x^{2} + x (3 x) + x \cdot 2 + 1 x^{2} + 1 (3 x) + 1 \cdot 2$

Step 3

Simplify terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

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

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Step 3.1.1.1

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

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Step 3.1.1.1.1

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

$x^{1} x^{2} + x (3 x) + x \cdot 2 + 1 x^{2} + 1 (3 x) + 1 \cdot 2$

Step 3.1.1.1.2

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

$x^{1 + 2} + x (3 x) + x \cdot 2 + 1 x^{2} + 1 (3 x) + 1 \cdot 2$

Step 3.1.1.2

Add $1$ and $2$ .

$x^{3} + x (3 x) + x \cdot 2 + 1 x^{2} + 1 (3 x) + 1 \cdot 2$

Step 3.1.2

Rewrite using the commutative property of multiplication.

$x^{3} + 3 x \cdot x + x \cdot 2 + 1 x^{2} + 1 (3 x) + 1 \cdot 2$

Step 3.1.3

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

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Step 3.1.3.1

Move $x$ .

$x^{3} + 3 (x \cdot x) + x \cdot 2 + 1 x^{2} + 1 (3 x) + 1 \cdot 2$

Step 3.1.3.2

Multiply $x$ by $x$ .

$x^{3} + 3 x^{2} + x \cdot 2 + 1 x^{2} + 1 (3 x) + 1 \cdot 2$

Step 3.1.4

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

$x^{3} + 3 x^{2} + 2 \cdot x + 1 x^{2} + 1 (3 x) + 1 \cdot 2$

Step 3.1.5

Multiply $x^{2}$ by $1$ .

$x^{3} + 3 x^{2} + 2 x + x^{2} + 1 (3 x) + 1 \cdot 2$

Step 3.1.6

Multiply $3 x$ by $1$ .

$x^{3} + 3 x^{2} + 2 x + x^{2} + 3 x + 1 \cdot 2$

Step 3.1.7

Multiply $2$ by $1$ .

$x^{3} + 3 x^{2} + 2 x + x^{2} + 3 x + 2$

Step 3.2

Simplify by adding terms.

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Step 3.2.1

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

$x^{3} + 4 x^{2} + 2 x + 3 x + 2$

Step 3.2.2

Add $2 x$ and $3 x$ .

$x^{3} + 4 x^{2} + 5 x + 2$