Factor x^2+1/2x+1/16

$x^{2} + \frac{1}{2} x + \frac{1}{16}$

Step 1

Rewrite the middle term.

$x^{2} + 2 x \frac{1}{4} + 0 + \frac{1}{16}$

Step 2

Rearrange terms.

$x^{2} + 2 x \frac{1}{4} + \frac{1}{16} + 0$

Step 3

Factor first three terms by perfect square rule.

${(x + \frac{1}{4})}^{2} + 0$

Step 4

Rewrite ${(x + \frac{1}{4})}^{2}$ as $(x + \frac{1}{4}) (x + \frac{1}{4})$ .

$(x + \frac{1}{4}) (x + \frac{1}{4}) + 0$

Step 5

Expand $(x + \frac{1}{4}) (x + \frac{1}{4})$ using the FOIL Method.

Apply the distributive property.

$x (x + \frac{1}{4}) + \frac{1}{4} (x + \frac{1}{4}) + 0$

Apply the distributive property.

$x \cdot x + x \frac{1}{4} + \frac{1}{4} (x + \frac{1}{4}) + 0$

Apply the distributive property.

$x \cdot x + x \frac{1}{4} + \frac{1}{4} x + \frac{1}{4} \cdot \frac{1}{4} + 0$

Step 6

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \frac{1}{4} + \frac{1}{4} x + \frac{1}{4} \cdot \frac{1}{4} + 0$

Combine $x$ and $\frac{1}{4}$ .

$x^{2} + \frac{x}{4} + \frac{1}{4} x + \frac{1}{4} \cdot \frac{1}{4} + 0$

Combine $\frac{1}{4}$ and $x$ .

$x^{2} + \frac{x}{4} + \frac{x}{4} + \frac{1}{4} \cdot \frac{1}{4} + 0$

Multiply $\frac{1}{4} \cdot \frac{1}{4}$ .

Multiply $\frac{1}{4}$ by $\frac{1}{4}$ .

$x^{2} + \frac{x}{4} + \frac{x}{4} + \frac{1}{4 \cdot 4} + 0$

Multiply $4$ by $4$ .

$x^{2} + \frac{x}{4} + \frac{x}{4} + \frac{1}{16} + 0$

Add $\frac{x}{4}$ and $\frac{x}{4}$ .

$x^{2} + 2 \frac{x}{4} + \frac{1}{16} + 0$

Step 7

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$x^{2} + 2 \frac{x}{2 (2)} + \frac{1}{16} + 0$

Cancel the common factor.

$x^{2} + 2 \frac{x}{2 \cdot 2} + \frac{1}{16} + 0$

Rewrite the expression.

$x^{2} + \frac{x}{2} + \frac{1}{16} + 0$

Step 8

Add $x^{2} + \frac{x}{2} + \frac{1}{16}$ and $0$ .

$x^{2} + \frac{x}{2} + \frac{1}{16}$

Step 9

Factor using the perfect square rule.

Rewrite $1$ as $1^{2}$ .

$x^{2} + \frac{x}{2} + \frac{1^{2}}{16}$

Rewrite $16$ as $4^{2}$ .

$x^{2} + \frac{x}{2} + \frac{1^{2}}{4^{2}}$

Rewrite $\frac{1^{2}}{4^{2}}$ as ${(\frac{1}{4})}^{2}$ .

$x^{2} + \frac{x}{2} + {(\frac{1}{4})}^{2}$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$\frac{x}{2} = 2 \cdot x \cdot \frac{1}{4}$

Rewrite the polynomial.

$x^{2} + 2 \cdot x \cdot \frac{1}{4} + {(\frac{1}{4})}^{2}$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = \frac{1}{4}$ .

${(x + \frac{1}{4})}^{2}$

Factor x^2+1/2x+1/16

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