Basic Math Examples

$(y + z) (2 y + 2 z)$

Step 1

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

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Step 1.1

Apply the distributive property.

$y (2 y + 2 z) + z (2 y + 2 z)$

Step 1.2

Apply the distributive property.

$y (2 y) + y (2 z) + z (2 y + 2 z)$

Step 1.3

Apply the distributive property.

$y (2 y) + y (2 z) + z (2 y) + z (2 z)$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$2 y \cdot y + y (2 z) + z (2 y) + z (2 z)$

Step 2.1.2

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

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Step 2.1.2.1

Move $y$ .

$2 (y \cdot y) + y (2 z) + z (2 y) + z (2 z)$

Step 2.1.2.2

Multiply $y$ by $y$ .

$2 y^{2} + y (2 z) + z (2 y) + z (2 z)$

Step 2.1.3

Rewrite using the commutative property of multiplication.

$2 y^{2} + 2 y z + z (2 y) + z (2 z)$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$2 y^{2} + 2 y z + 2 z y + z (2 z)$

Step 2.1.5

Rewrite using the commutative property of multiplication.

$2 y^{2} + 2 y z + 2 z y + 2 z \cdot z$

Step 2.1.6

Multiply $z$ by $z$ by adding the exponents.

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Step 2.1.6.1

Move $z$ .

$2 y^{2} + 2 y z + 2 z y + 2 (z \cdot z)$

Step 2.1.6.2

Multiply $z$ by $z$ .

$2 y^{2} + 2 y z + 2 z y + 2 z^{2}$

Step 2.2

Add $2 y z$ and $2 z y$ .

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Step 2.2.1

Move $z$ .

$2 y^{2} + 2 y z + 2 y z + 2 z^{2}$

Step 2.2.2

Add $2 y z$ and $2 y z$ .

$2 y^{2} + 4 y z + 2 z^{2}$