Basic Math Examples

${(4 x^{5} + 2)}^{2}$

Step 1

Rewrite ${(4 x^{5} + 2)}^{2}$ as $(4 x^{5} + 2) (4 x^{5} + 2)$ .

$(4 x^{5} + 2) (4 x^{5} + 2)$

Step 2

Expand $(4 x^{5} + 2) (4 x^{5} + 2)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$4 x^{5} (4 x^{5} + 2) + 2 (4 x^{5} + 2)$

Step 2.2

Apply the distributive property.

$4 x^{5} (4 x^{5}) + 4 x^{5} \cdot 2 + 2 (4 x^{5} + 2)$

Step 2.3

Apply the distributive property.

$4 x^{5} (4 x^{5}) + 4 x^{5} \cdot 2 + 2 (4 x^{5}) + 2 \cdot 2$

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

Rewrite using the commutative property of multiplication.

$4 \cdot 4 x^{5} x^{5} + 4 x^{5} \cdot 2 + 2 (4 x^{5}) + 2 \cdot 2$

Step 3.1.2

Multiply $x^{5}$ by $x^{5}$ by adding the exponents.

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Step 3.1.2.1

Move $x^{5}$ .

$4 \cdot 4 (x^{5} x^{5}) + 4 x^{5} \cdot 2 + 2 (4 x^{5}) + 2 \cdot 2$

Step 3.1.2.2

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

$4 \cdot 4 x^{5 + 5} + 4 x^{5} \cdot 2 + 2 (4 x^{5}) + 2 \cdot 2$

Step 3.1.2.3

Add $5$ and $5$ .

$4 \cdot 4 x^{10} + 4 x^{5} \cdot 2 + 2 (4 x^{5}) + 2 \cdot 2$

Step 3.1.3

Multiply $4$ by $4$ .

$16 x^{10} + 4 x^{5} \cdot 2 + 2 (4 x^{5}) + 2 \cdot 2$

Step 3.1.4

Multiply $2$ by $4$ .

$16 x^{10} + 8 x^{5} + 2 (4 x^{5}) + 2 \cdot 2$

Step 3.1.5

Multiply $4$ by $2$ .

$16 x^{10} + 8 x^{5} + 8 x^{5} + 2 \cdot 2$

Step 3.1.6

Multiply $2$ by $2$ .

$16 x^{10} + 8 x^{5} + 8 x^{5} + 4$

Step 3.2

Add $8 x^{5}$ and $8 x^{5}$ .

$16 x^{10} + 16 x^{5} + 4$