Basic Math Examples

${(6 e - 4 y)}^{2}$

Step 1

Rewrite ${(6 e - 4 y)}^{2}$ as $(6 e - 4 y) (6 e - 4 y)$ .

$(6 e - 4 y) (6 e - 4 y)$

Step 2

Expand $(6 e - 4 y) (6 e - 4 y)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$6 e (6 e - 4 y) - 4 y (6 e - 4 y)$

Step 2.2

Apply the distributive property.

$6 e (6 e) + 6 e (- 4 y) - 4 y (6 e - 4 y)$

Step 2.3

Apply the distributive property.

$6 e (6 e) + 6 e (- 4 y) - 4 y (6 e) - 4 y (- 4 y)$

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 $6 e (6 e)$ .

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Step 3.1.1.1

Multiply $6$ by $6$ .

$36 e e + 6 e (- 4 y) - 4 y (6 e) - 4 y (- 4 y)$

Step 3.1.1.2

Raise $e$ to the power of $1$ .

$36 (e^{1} e) + 6 e (- 4 y) - 4 y (6 e) - 4 y (- 4 y)$

Step 3.1.1.3

Raise $e$ to the power of $1$ .

$36 (e^{1} e^{1}) + 6 e (- 4 y) - 4 y (6 e) - 4 y (- 4 y)$

Step 3.1.1.4

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

$36 e^{1 + 1} + 6 e (- 4 y) - 4 y (6 e) - 4 y (- 4 y)$

Step 3.1.1.5

Add $1$ and $1$ .

$36 e^{2} + 6 e (- 4 y) - 4 y (6 e) - 4 y (- 4 y)$

Step 3.1.2

Multiply $- 4$ by $6$ .

$36 e^{2} - 24 e y - 4 y (6 e) - 4 y (- 4 y)$

Step 3.1.3

Multiply $6$ by $- 4$ .

$36 e^{2} - 24 e y - 24 y e - 4 y (- 4 y)$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$36 e^{2} - 24 e y - 24 y e - 4 \cdot - 4 y \cdot y$

Step 3.1.5

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

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Step 3.1.5.1

Move $y$ .

$36 e^{2} - 24 e y - 24 y e - 4 \cdot - 4 (y \cdot y)$

Step 3.1.5.2

Multiply $y$ by $y$ .

$36 e^{2} - 24 e y - 24 y e - 4 \cdot - 4 y^{2}$

Step 3.1.6

Multiply $- 4$ by $- 4$ .

$36 e^{2} - 24 e y - 24 y e + 16 y^{2}$

Step 3.2

Subtract $24 y e$ from $- 24 e y$ .

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Step 3.2.1

Move $e$ .

$36 e^{2} - 24 y e - 24 y e + 16 y^{2}$

Step 3.2.2

Subtract $24 y e$ from $- 24 y e$ .

$36 e^{2} - 48 y e + 16 y^{2}$

Step 4

Move $36 e^{2}$ .

$- 48 y e + 16 y^{2} + 36 e^{2}$

Step 5

Reorder $- 48 y e$ and $16 y^{2}$ .

$16 y^{2} - 48 y e + 36 e^{2}$