Basic Math Examples

$2 {(8 + 3 y)}^{2}$

Step 1

Rewrite ${(8 + 3 y)}^{2}$ as $(8 + 3 y) (8 + 3 y)$ .

$2 ((8 + 3 y) (8 + 3 y))$

Step 2

Expand $(8 + 3 y) (8 + 3 y)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$2 (8 (8 + 3 y) + 3 y (8 + 3 y))$

Step 2.2

Apply the distributive property.

$2 (8 \cdot 8 + 8 (3 y) + 3 y (8 + 3 y))$

Step 2.3

Apply the distributive property.

$2 (8 \cdot 8 + 8 (3 y) + 3 y \cdot 8 + 3 y (3 y))$

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

Multiply $8$ by $8$ .

$2 (64 + 8 (3 y) + 3 y \cdot 8 + 3 y (3 y))$

Step 3.1.2

Multiply $3$ by $8$ .

$2 (64 + 24 y + 3 y \cdot 8 + 3 y (3 y))$

Step 3.1.3

Multiply $8$ by $3$ .

$2 (64 + 24 y + 24 y + 3 y (3 y))$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$2 (64 + 24 y + 24 y + 3 \cdot 3 y \cdot y)$

Step 3.1.5

Multiply $y$ by $y$ by adding the exponents.

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Step 3.1.5.1

Move $y$ .

$2 (64 + 24 y + 24 y + 3 \cdot 3 (y \cdot y))$

Step 3.1.5.2

Multiply $y$ by $y$ .

$2 (64 + 24 y + 24 y + 3 \cdot 3 y^{2})$

Step 3.1.6

Multiply $3$ by $3$ .

$2 (64 + 24 y + 24 y + 9 y^{2})$

Step 3.2

Add $24 y$ and $24 y$ .

$2 (64 + 48 y + 9 y^{2})$

Step 4

Apply the distributive property.

$2 \cdot 64 + 2 (48 y) + 2 (9 y^{2})$

Step 5

Simplify.

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Step 5.1

Multiply $2$ by $64$ .

$128 + 2 (48 y) + 2 (9 y^{2})$

Step 5.2

Multiply $48$ by $2$ .

$128 + 96 y + 2 (9 y^{2})$

Step 5.3

Multiply $9$ by $2$ .

$128 + 96 y + 18 y^{2}$