Trigonometry Examples

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

Step 1

Rewrite

${(x + 5)}^{2}$ as

$(x + 5) (x + 5)$ .

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

Step 2

Expand

$(x + 5) (x + 5)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

$x \cdot x + x \cdot 5 + 5 (x + 5) = x^{2} + 10 x + 25$

Step 2.3

Apply the distributive property.

$x \cdot x + x \cdot 5 + 5 x + 5 \cdot 5 = x^{2} + 10 x + 25$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply

$x$ by

$x$ .

$x^{2} + x \cdot 5 + 5 x + 5 \cdot 5 = x^{2} + 10 x + 25$

Step 3.1.2

Move

$5$ to the left of

$x$ .

$x^{2} + 5 \cdot x + 5 x + 5 \cdot 5 = x^{2} + 10 x + 25$

Step 3.1.3

Multiply

$5$ by

$5$ .

$x^{2} + 5 x + 5 x + 25 = x^{2} + 10 x + 25$

Step 3.2

Add

$5 x$ and

$5 x$ .

$x^{2} + 10 x + 25 = x^{2} + 10 x + 25$

Step 4

Since the two sides have been shown to be equivalent, the equation is an identity.

${(x + 5)}^{2} = x^{2} + 10 x + 25$ is an identity.