Algebra Examples

${(x + 2)}^{3} = x (x^{2} - 10 x + 25)$

Step 1

Subtract $x (x^{2} - 10 x + 25)$ from both sides of the equation.

${(x + 2)}^{3} - x (x^{2} - 10 x + 25) = 0$

Step 2

Simplify ${(x + 2)}^{3} - x (x^{2} - 10 x + 25)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Use the Binomial Theorem.

$x^{3} + 3 x^{2} \cdot 2 + 3 x \cdot 2^{2} + 2^{3} - x (x^{2} - 10 x + 25) = 0$

Step 2.1.2

Simplify each term.

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Step 2.1.2.1

Multiply $2$ by $3$ .

$x^{3} + 6 x^{2} + 3 x \cdot 2^{2} + 2^{3} - x (x^{2} - 10 x + 25) = 0$

Step 2.1.2.2

Raise $2$ to the power of $2$ .

$x^{3} + 6 x^{2} + 3 x \cdot 4 + 2^{3} - x (x^{2} - 10 x + 25) = 0$

Step 2.1.2.3

Multiply $4$ by $3$ .

$x^{3} + 6 x^{2} + 12 x + 2^{3} - x (x^{2} - 10 x + 25) = 0$

Step 2.1.2.4

Raise $2$ to the power of $3$ .

$x^{3} + 6 x^{2} + 12 x + 8 - x (x^{2} - 10 x + 25) = 0$

Step 2.1.3

Apply the distributive property.

$x^{3} + 6 x^{2} + 12 x + 8 - x \cdot x^{2} - x (- 10 x) - x \cdot 25 = 0$

Step 2.1.4

Simplify.

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Step 2.1.4.1

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

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Step 2.1.4.1.1

Move $x^{2}$ .

$x^{3} + 6 x^{2} + 12 x + 8 - (x^{2} x) - x (- 10 x) - x \cdot 25 = 0$

Step 2.1.4.1.2

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

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Step 2.1.4.1.2.1

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

$x^{3} + 6 x^{2} + 12 x + 8 - (x^{2} x^{1}) - x (- 10 x) - x \cdot 25 = 0$

Step 2.1.4.1.2.2

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

$x^{3} + 6 x^{2} + 12 x + 8 - x^{2 + 1} - x (- 10 x) - x \cdot 25 = 0$

Step 2.1.4.1.3

Add $2$ and $1$ .

$x^{3} + 6 x^{2} + 12 x + 8 - x^{3} - x (- 10 x) - x \cdot 25 = 0$

Step 2.1.4.2

Rewrite using the commutative property of multiplication.

$x^{3} + 6 x^{2} + 12 x + 8 - x^{3} - 1 \cdot - 10 x \cdot x - x \cdot 25 = 0$

Step 2.1.4.3

Multiply $25$ by $- 1$ .

$x^{3} + 6 x^{2} + 12 x + 8 - x^{3} - 1 \cdot - 10 x \cdot x - 25 x = 0$

Step 2.1.5

Simplify each term.

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Step 2.1.5.1

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

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Step 2.1.5.1.1

Move $x$ .

$x^{3} + 6 x^{2} + 12 x + 8 - x^{3} - 1 \cdot - 10 (x \cdot x) - 25 x = 0$

Step 2.1.5.1.2

Multiply $x$ by $x$ .

$x^{3} + 6 x^{2} + 12 x + 8 - x^{3} - 1 \cdot - 10 x^{2} - 25 x = 0$

Step 2.1.5.2

Multiply $- 1$ by $- 10$ .

$x^{3} + 6 x^{2} + 12 x + 8 - x^{3} + 10 x^{2} - 25 x = 0$

Step 2.2

Combine the opposite terms in $x^{3} + 6 x^{2} + 12 x + 8 - x^{3} + 10 x^{2} - 25 x$ .

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Step 2.2.1

Subtract $x^{3}$ from $x^{3}$ .

$6 x^{2} + 12 x + 8 + 0 + 10 x^{2} - 25 x = 0$

Step 2.2.2

Add $6 x^{2} + 12 x + 8$ and $0$ .

$6 x^{2} + 12 x + 8 + 10 x^{2} - 25 x = 0$

Step 2.3

Add $6 x^{2}$ and $10 x^{2}$ .

$16 x^{2} + 12 x + 8 - 25 x = 0$

Step 2.4

Subtract $25 x$ from $12 x$ .

$16 x^{2} - 13 x + 8 = 0$

Step 3

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c = 0$

Step 4

The standard form is $16 x^{2} - 13 x + 8$ .

$16 x^{2} - 13 x + 8 = 0$

Step 5