Finite Math Examples

${(a + 10)}^{2}$

Step 1

Rewrite ${(a + 10)}^{2}$ as $(a + 10) (a + 10)$ .

$(a + 10) (a + 10)$

Step 2

Expand $(a + 10) (a + 10)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$a (a + 10) + 10 (a + 10)$

Step 2.2

Apply the distributive property.

$a \cdot a + a \cdot 10 + 10 (a + 10)$

Step 2.3

Apply the distributive property.

$a \cdot a + a \cdot 10 + 10 a + 10 \cdot 10$

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 $a$ by $a$ .

$a^{2} + a \cdot 10 + 10 a + 10 \cdot 10$

Step 3.1.2

Move $10$ to the left of $a$ .

$a^{2} + 10 \cdot a + 10 a + 10 \cdot 10$

Step 3.1.3

Multiply $10$ by $10$ .

$a^{2} + 10 a + 10 a + 100$

Step 3.2

Add $10 a$ and $10 a$ .

$a^{2} + 20 a + 100$

Step 4

Factor using the perfect square rule.

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Step 4.1

Rewrite $100$ as $10^{2}$ .

$a^{2} + 20 a + 10^{2}$

Step 4.2

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

$20 a = 2 \cdot a \cdot 10$

Step 4.3

Rewrite the polynomial.

$a^{2} + 2 \cdot a \cdot 10 + 10^{2}$

Step 4.4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = a$ and $b = 10$ .

${(a + 10)}^{2}$