Basic Math Examples

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

Step 1

Multiply $x + 2$ by ${(x + 2)}^{5}$ by adding the exponents.

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Step 1.1

Multiply $x + 2$ by ${(x + 2)}^{5}$ .

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Step 1.1.1

Raise $x + 2$ to the power of $1$ .

${(x + 2)}^{1} {(x + 2)}^{5}$

Step 1.1.2

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

${(x + 2)}^{1 + 5}$

Step 1.2

Add $1$ and $5$ .

${(x + 2)}^{6}$

Step 2

Use the Binomial Theorem.

$x^{6} + 6 x^{5} \cdot 2 + 15 x^{4} \cdot 2^{2} + 20 x^{3} \cdot 2^{3} + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}$

Step 3

Simplify each term.

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Step 3.1

Multiply $2$ by $6$ .

$x^{6} + 12 x^{5} + 15 x^{4} \cdot 2^{2} + 20 x^{3} \cdot 2^{3} + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}$

Step 3.2

Raise $2$ to the power of $2$ .

$x^{6} + 12 x^{5} + 15 x^{4} \cdot 4 + 20 x^{3} \cdot 2^{3} + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}$

Step 3.3

Multiply $4$ by $15$ .

$x^{6} + 12 x^{5} + 60 x^{4} + 20 x^{3} \cdot 2^{3} + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}$

Step 3.4

Raise $2$ to the power of $3$ .

$x^{6} + 12 x^{5} + 60 x^{4} + 20 x^{3} \cdot 8 + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}$

Step 3.5

Multiply $8$ by $20$ .

$x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}$

Step 3.6

Raise $2$ to the power of $4$ .

$x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 15 x^{2} \cdot 16 + 6 x \cdot 2^{5} + 2^{6}$

Step 3.7

Multiply $16$ by $15$ .

$x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 240 x^{2} + 6 x \cdot 2^{5} + 2^{6}$

Step 3.8

Raise $2$ to the power of $5$ .

$x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 240 x^{2} + 6 x \cdot 32 + 2^{6}$

Step 3.9

Multiply $32$ by $6$ .

$x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 240 x^{2} + 192 x + 2^{6}$

Step 3.10

Raise $2$ to the power of $6$ .

$x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 240 x^{2} + 192 x + 64$