Basic Math Examples

$(7 x^{2} + 5) (x + 1)$

Step 1

Expand $(7 x^{2} + 5) (x + 1)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$7 x^{2} (x + 1) + 5 (x + 1)$

Step 1.2

Apply the distributive property.

$7 x^{2} x + 7 x^{2} \cdot 1 + 5 (x + 1)$

Step 1.3

Apply the distributive property.

$7 x^{2} x + 7 x^{2} \cdot 1 + 5 x + 5 \cdot 1$

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Move $x$ .

$7 (x \cdot x^{2}) + 7 x^{2} \cdot 1 + 5 x + 5 \cdot 1$

Step 2.1.2

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

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Step 2.1.2.1

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

$7 (x^{1} x^{2}) + 7 x^{2} \cdot 1 + 5 x + 5 \cdot 1$

Step 2.1.2.2

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

$7 x^{1 + 2} + 7 x^{2} \cdot 1 + 5 x + 5 \cdot 1$

Step 2.1.3

Add $1$ and $2$ .

$7 x^{3} + 7 x^{2} \cdot 1 + 5 x + 5 \cdot 1$

Step 2.2

Multiply $7$ by $1$ .

$7 x^{3} + 7 x^{2} + 5 x + 5 \cdot 1$

Step 2.3

Multiply $5$ by $1$ .

$7 x^{3} + 7 x^{2} + 5 x + 5$