Pre-Algebra Examples

$(5 x^{2} + 30 x + 20) (x + 5)$

Step 1

Write $(5 x^{2} + 30 x + 20) (x + 5)$ as an equation.

$y = (5 x^{2} + 30 x + 20) (x + 5)$

Step 2

Expand $(5 x^{2} + 30 x + 20) (x + 5)$ by multiplying each term in the first expression by each term in the second expression.

$y = 5 x^{2} x + 5 x^{2} \cdot 5 + 30 x \cdot x + 30 x \cdot 5 + 20 x + 20 \cdot 5$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $x$ .

$y = 5 (x \cdot x^{2}) + 5 x^{2} \cdot 5 + 30 x \cdot x + 30 x \cdot 5 + 20 x + 20 \cdot 5$

Step 3.1.2

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

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Step 3.1.2.1

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

$y = 5 (x^{1} x^{2}) + 5 x^{2} \cdot 5 + 30 x \cdot x + 30 x \cdot 5 + 20 x + 20 \cdot 5$

Step 3.1.2.2

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

$y = 5 x^{1 + 2} + 5 x^{2} \cdot 5 + 30 x \cdot x + 30 x \cdot 5 + 20 x + 20 \cdot 5$

Step 3.1.3

Add $1$ and $2$ .

$y = 5 x^{3} + 5 x^{2} \cdot 5 + 30 x \cdot x + 30 x \cdot 5 + 20 x + 20 \cdot 5$

Step 3.2

Multiply $5$ by $5$ .

$y = 5 x^{3} + 25 x^{2} + 30 x \cdot x + 30 x \cdot 5 + 20 x + 20 \cdot 5$

Step 3.3

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

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Step 3.3.1

Move $x$ .

$y = 5 x^{3} + 25 x^{2} + 30 (x \cdot x) + 30 x \cdot 5 + 20 x + 20 \cdot 5$

Step 3.3.2

Multiply $x$ by $x$ .

$y = 5 x^{3} + 25 x^{2} + 30 x^{2} + 30 x \cdot 5 + 20 x + 20 \cdot 5$

Step 3.4

Multiply $5$ by $30$ .

$y = 5 x^{3} + 25 x^{2} + 30 x^{2} + 150 x + 20 x + 20 \cdot 5$

Step 3.5

Multiply $20$ by $5$ .

$y = 5 x^{3} + 25 x^{2} + 30 x^{2} + 150 x + 20 x + 100$

Step 4

Add $25 x^{2}$ and $30 x^{2}$ .

$y = 5 x^{3} + 55 x^{2} + 150 x + 20 x + 100$

Step 5

Add $150 x$ and $20 x$ .

$y = 5 x^{3} + 55 x^{2} + 170 x + 100$

Step 6

The given equation $y = 5 x^{3} + 55 x^{2} + 170 x + 100$ can not be written as $y = k x^{2}$ , so $y$ doesn't vary directly with $x^{2}$ .

$y$ doesn't vary directly with $x$