Algebra Examples

8 x^{3} - 125

$8 x^{3} - 125$

Step 1

Rewrite

8 x^{3}

$8 x^{3}$ as

{(2 x)}^{3}

${(2 x)}^{3}$ .

{(2 x)}^{3} - 125

${(2 x)}^{3} - 125$

Step 2

Rewrite

125

$125$ as

5^{3}

$5^{3}$ .

{(2 x)}^{3} - 5^{3}

${(2 x)}^{3} - 5^{3}$

Step 3

Since both terms are perfect cubes, factor using the difference of cubes formula,

a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})

$a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where

a = 2 x

$a = 2 x$ and

b = 5

$b = 5$ .

(2 x - 5) ({(2 x)}^{2} + 2 x \cdot 5 + 5^{2})

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

Step 4

Simplify.

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Step 4.1

Apply the product rule to

2 x

$2 x$ .

(2 x - 5) (2^{2} x^{2} + 2 x \cdot 5 + 5^{2})

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

Step 4.2

Raise

2

$2$ to the power of

2

$2$ .

(2 x - 5) (4 x^{2} + 2 x \cdot 5 + 5^{2})

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

Step 4.3

Multiply

5

$5$ by

2

$2$ .

(2 x - 5) (4 x^{2} + 10 x + 5^{2})

$(2 x - 5) (4 x^{2} + 10 x + 5^{2})$

Step 4.4

Raise

5

$5$ to the power of

2

$2$ .

(2 x - 5) (4 x^{2} + 10 x + 25)

$(2 x - 5) (4 x^{2} + 10 x + 25)$

(2 x - 5) (4 x^{2} + 10 x + 25)

$(2 x - 5) (4 x^{2} + 10 x + 25)$