Algebra Examples

$(4 x^{4} + 3 x^{2} - 1) + (m x^{3} + 2) (3 x^{2} + 1)$

Step 1

Simplify each term.

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Step 1.1

Expand $(m x^{3} + 2) (3 x^{2} + 1)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$4 x^{4} + 3 x^{2} - 1 + m x^{3} (3 x^{2} + 1) + 2 (3 x^{2} + 1)$

Step 1.1.2

Apply the distributive property.

$4 x^{4} + 3 x^{2} - 1 + m x^{3} (3 x^{2}) + m x^{3} \cdot 1 + 2 (3 x^{2} + 1)$

Step 1.1.3

Apply the distributive property.

$4 x^{4} + 3 x^{2} - 1 + m x^{3} (3 x^{2}) + m x^{3} \cdot 1 + 2 (3 x^{2}) + 2 \cdot 1$

Step 1.2

Simplify each term.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$4 x^{4} + 3 x^{2} - 1 + 3 m x^{3} x^{2} + m x^{3} \cdot 1 + 2 (3 x^{2}) + 2 \cdot 1$

Step 1.2.2

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

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Step 1.2.2.1

Move $x^{2}$ .

$4 x^{4} + 3 x^{2} - 1 + 3 m (x^{2} x^{3}) + m x^{3} \cdot 1 + 2 (3 x^{2}) + 2 \cdot 1$

Step 1.2.2.2

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

$4 x^{4} + 3 x^{2} - 1 + 3 m x^{2 + 3} + m x^{3} \cdot 1 + 2 (3 x^{2}) + 2 \cdot 1$

Step 1.2.2.3

Add $2$ and $3$ .

$4 x^{4} + 3 x^{2} - 1 + 3 m x^{5} + m x^{3} \cdot 1 + 2 (3 x^{2}) + 2 \cdot 1$

Step 1.2.3

Multiply $m$ by $1$ .

$4 x^{4} + 3 x^{2} - 1 + 3 m x^{5} + m x^{3} + 2 (3 x^{2}) + 2 \cdot 1$

Step 1.2.4

Multiply $3$ by $2$ .

$4 x^{4} + 3 x^{2} - 1 + 3 m x^{5} + m x^{3} + 6 x^{2} + 2 \cdot 1$

Step 1.2.5

Multiply $2$ by $1$ .

$4 x^{4} + 3 x^{2} - 1 + 3 m x^{5} + m x^{3} + 6 x^{2} + 2$

Step 2

Simplify by adding terms.

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Step 2.1

Add $3 x^{2}$ and $6 x^{2}$ .

$4 x^{4} + 9 x^{2} - 1 + 3 m x^{5} + m x^{3} + 2$

Step 2.2

Add $- 1$ and $2$ .

$4 x^{4} + 9 x^{2} + 3 m x^{5} + m x^{3} + 1$