Basic Math Examples

${((7 \cdot - 2) + 2 y)}^{2}$

Step 1

Simplify the expression.

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Step 1.1

Multiply $7$ by $- 2$ .

${(- 14 + 2 y)}^{2}$

Step 1.2

Rewrite ${(- 14 + 2 y)}^{2}$ as $(- 14 + 2 y) (- 14 + 2 y)$ .

$(- 14 + 2 y) (- 14 + 2 y)$

Step 2

Expand $(- 14 + 2 y) (- 14 + 2 y)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$- 14 (- 14 + 2 y) + 2 y (- 14 + 2 y)$

Step 2.2

Apply the distributive property.

$- 14 \cdot - 14 - 14 (2 y) + 2 y (- 14 + 2 y)$

Step 2.3

Apply the distributive property.

$- 14 \cdot - 14 - 14 (2 y) + 2 y \cdot - 14 + 2 y (2 y)$

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 $- 14$ by $- 14$ .

$196 - 14 (2 y) + 2 y \cdot - 14 + 2 y (2 y)$

Step 3.1.2

Multiply $2$ by $- 14$ .

$196 - 28 y + 2 y \cdot - 14 + 2 y (2 y)$

Step 3.1.3

Multiply $- 14$ by $2$ .

$196 - 28 y - 28 y + 2 y (2 y)$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$196 - 28 y - 28 y + 2 \cdot 2 y \cdot y$

Step 3.1.5

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

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Step 3.1.5.1

Move $y$ .

$196 - 28 y - 28 y + 2 \cdot 2 (y \cdot y)$

Step 3.1.5.2

Multiply $y$ by $y$ .

$196 - 28 y - 28 y + 2 \cdot 2 y^{2}$

Step 3.1.6

Multiply $2$ by $2$ .

$196 - 28 y - 28 y + 4 y^{2}$

Step 3.2

Subtract $28 y$ from $- 28 y$ .

$196 - 56 y + 4 y^{2}$