Pre-Algebra Examples

$(x - 5) (x^{2} + 5 x + 25) = 0$

Step 1

Simplify $(x - 5) (x^{2} + 5 x + 25)$ .

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Step 1.1

Expand $(x - 5) (x^{2} + 5 x + 25)$ by multiplying each term in the first expression by each term in the second expression.

$x \cdot x^{2} + x (5 x) + x \cdot 25 - 5 x^{2} - 5 (5 x) - 5 \cdot 25 = 0$

Step 1.2

Simplify terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

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

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Step 1.2.1.1.1

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

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Step 1.2.1.1.1.1

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

$x^{1} x^{2} + x (5 x) + x \cdot 25 - 5 x^{2} - 5 (5 x) - 5 \cdot 25 = 0$

Step 1.2.1.1.1.2

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

$x^{1 + 2} + x (5 x) + x \cdot 25 - 5 x^{2} - 5 (5 x) - 5 \cdot 25 = 0$

Step 1.2.1.1.2

Add $1$ and $2$ .

$x^{3} + x (5 x) + x \cdot 25 - 5 x^{2} - 5 (5 x) - 5 \cdot 25 = 0$

Step 1.2.1.2

Rewrite using the commutative property of multiplication.

$x^{3} + 5 x \cdot x + x \cdot 25 - 5 x^{2} - 5 (5 x) - 5 \cdot 25 = 0$

Step 1.2.1.3

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

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Step 1.2.1.3.1

Move $x$ .

$x^{3} + 5 (x \cdot x) + x \cdot 25 - 5 x^{2} - 5 (5 x) - 5 \cdot 25 = 0$

Step 1.2.1.3.2

Multiply $x$ by $x$ .

$x^{3} + 5 x^{2} + x \cdot 25 - 5 x^{2} - 5 (5 x) - 5 \cdot 25 = 0$

Step 1.2.1.4

Move $25$ to the left of $x$ .

$x^{3} + 5 x^{2} + 25 \cdot x - 5 x^{2} - 5 (5 x) - 5 \cdot 25 = 0$

Step 1.2.1.5

Multiply $5$ by $- 5$ .

$x^{3} + 5 x^{2} + 25 x - 5 x^{2} - 25 x - 5 \cdot 25 = 0$

Step 1.2.1.6

Multiply $- 5$ by $25$ .

$x^{3} + 5 x^{2} + 25 x - 5 x^{2} - 25 x - 125 = 0$

Step 1.2.2

Combine the opposite terms in $x^{3} + 5 x^{2} + 25 x - 5 x^{2} - 25 x - 125$ .

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Step 1.2.2.1

Subtract $5 x^{2}$ from $5 x^{2}$ .

$x^{3} + 25 x + 0 - 25 x - 125 = 0$

Step 1.2.2.2

Add $x^{3} + 25 x$ and $0$ .

$x^{3} + 25 x - 25 x - 125 = 0$

Step 1.2.2.3

Subtract $25 x$ from $25 x$ .

$x^{3} + 0 - 125 = 0$

Step 1.2.2.4

Add $x^{3}$ and $0$ .

$x^{3} - 125 = 0$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = 5$

Step 3