Algebra Examples

${(e + 2 a + q)}^{2}$

Step 1

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

$(e + 2 a + q) (e + 2 a + q)$

Step 2

Expand $(e + 2 a + q) (e + 2 a + q)$ by multiplying each term in the first expression by each term in the second expression.

$e e + e (2 a) + e q + 2 a e + 2 a (2 a) + 2 a q + q e + q (2 a) + q \cdot q$

Step 3

Simplify each term.

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Step 3.1

Multiply $e e$ .

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Step 3.1.1

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

$e^{1} e + e (2 a) + e q + 2 a e + 2 a (2 a) + 2 a q + q e + q (2 a) + q \cdot q$

Step 3.1.2

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

$e^{1} e^{1} + e (2 a) + e q + 2 a e + 2 a (2 a) + 2 a q + q e + q (2 a) + q \cdot q$

Step 3.1.3

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

$e^{1 + 1} + e (2 a) + e q + 2 a e + 2 a (2 a) + 2 a q + q e + q (2 a) + q \cdot q$

Step 3.1.4

Add $1$ and $1$ .

$e^{2} + e (2 a) + e q + 2 a e + 2 a (2 a) + 2 a q + q e + q (2 a) + q \cdot q$

Step 3.2

Move $2$ to the left of $e$ .

$e^{2} + 2 \cdot e a + e q + 2 a e + 2 a (2 a) + 2 a q + q e + q (2 a) + q \cdot q$

Step 3.3

Rewrite using the commutative property of multiplication.

$e^{2} + 2 e a + e q + 2 a e + 2 \cdot 2 a \cdot a + 2 a q + q e + q (2 a) + q \cdot q$

Step 3.4

Multiply $a$ by $a$ by adding the exponents.

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Step 3.4.1

Move $a$ .

$e^{2} + 2 e a + e q + 2 a e + 2 \cdot 2 (a \cdot a) + 2 a q + q e + q (2 a) + q \cdot q$

Step 3.4.2

Multiply $a$ by $a$ .

$e^{2} + 2 e a + e q + 2 a e + 2 \cdot 2 a^{2} + 2 a q + q e + q (2 a) + q \cdot q$

Step 3.5

Multiply $2$ by $2$ .

$e^{2} + 2 e a + e q + 2 a e + 4 a^{2} + 2 a q + q e + q (2 a) + q \cdot q$

Step 3.6

Rewrite using the commutative property of multiplication.

$e^{2} + 2 e a + e q + 2 a e + 4 a^{2} + 2 a q + q e + 2 q a + q \cdot q$

Step 3.7

Multiply $q$ by $q$ .

$e^{2} + 2 e a + e q + 2 a e + 4 a^{2} + 2 a q + q e + 2 q a + q^{2}$

Step 4

Add $2 e a$ and $2 a e$ .

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Step 4.1

Move $e$ .

$e^{2} + 2 a e + 2 a e + e q + 4 a^{2} + 2 a q + q e + 2 q a + q^{2}$

Step 4.2

Add $2 a e$ and $2 a e$ .

$e^{2} + 4 a e + e q + 4 a^{2} + 2 a q + q e + 2 q a + q^{2}$

Step 5

Add $e q$ and $q e$ .

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Step 5.1

Reorder $e$ and $q$ .

$e^{2} + 4 a e + 4 a^{2} + 2 a q + q e + q e + 2 q a + q^{2}$

Step 5.2

Add $q e$ and $q e$ .

$e^{2} + 4 a e + 4 a^{2} + 2 a q + 2 q e + 2 q a + q^{2}$

Step 6

Add $2 a q$ and $2 q a$ .

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Step 6.1

Move $q$ .

$e^{2} + 4 a e + 4 a^{2} + 2 a q + 2 a q + 2 q e + q^{2}$

Step 6.2

Add $2 a q$ and $2 a q$ .

$e^{2} + 4 a e + 4 a^{2} + 4 a q + 2 q e + q^{2}$