Algebra Examples

${(3 x^{5} + y)}^{2}$

Step 1

Rewrite ${(3 x^{5} + y)}^{2}$ as $(3 x^{5} + y) (3 x^{5} + y)$ .

$(3 x^{5} + y) (3 x^{5} + y)$

Step 2

Expand $(3 x^{5} + y) (3 x^{5} + y)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$3 x^{5} (3 x^{5} + y) + y (3 x^{5} + y)$

Step 2.2

Apply the distributive property.

$3 x^{5} (3 x^{5}) + 3 x^{5} y + y (3 x^{5} + y)$

Step 2.3

Apply the distributive property.

$3 x^{5} (3 x^{5}) + 3 x^{5} y + y (3 x^{5}) + y \cdot y$

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.

$3 \cdot 3 x^{5} x^{5} + 3 x^{5} y + y (3 x^{5}) + y \cdot y$

Step 3.1.2

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

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Step 3.1.2.1

Move $x^{5}$ .

$3 \cdot 3 (x^{5} x^{5}) + 3 x^{5} y + y (3 x^{5}) + y \cdot y$

Step 3.1.2.2

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

$3 \cdot 3 x^{5 + 5} + 3 x^{5} y + y (3 x^{5}) + y \cdot y$

Step 3.1.2.3

Add $5$ and $5$ .

$3 \cdot 3 x^{10} + 3 x^{5} y + y (3 x^{5}) + y \cdot y$

Step 3.1.3

Multiply $3$ by $3$ .

$9 x^{10} + 3 x^{5} y + y (3 x^{5}) + y \cdot y$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$9 x^{10} + 3 x^{5} y + 3 y x^{5} + y \cdot y$

Step 3.1.5

Multiply $y$ by $y$ .

$9 x^{10} + 3 x^{5} y + 3 y x^{5} + y^{2}$

Step 3.2

Add $3 x^{5} y$ and $3 y x^{5}$ .

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Step 3.2.1

Move $y$ .

$9 x^{10} + 3 x^{5} y + 3 x^{5} y + y^{2}$

Step 3.2.2

Add $3 x^{5} y$ and $3 x^{5} y$ .

$9 x^{10} + 6 x^{5} y + y^{2}$