Basic Math Examples

$9 (5 z + 6 y) \cdot (5 (6 z + 5 y))$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$(9 (5 z) + 9 (6 y)) \cdot (5 (6 z + 5 y))$

Step 1.2

Multiply.

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Step 1.2.1

Multiply $5$ by $9$ .

$(45 z + 9 (6 y)) \cdot (5 (6 z + 5 y))$

Step 1.2.2

Multiply $6$ by $9$ .

$(45 z + 54 y) \cdot (5 (6 z + 5 y))$

Step 1.3

Apply the distributive property.

$(45 z + 54 y) \cdot (5 (6 z) + 5 (5 y))$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $6$ by $5$ .

$(45 z + 54 y) \cdot (30 z + 5 (5 y))$

Step 1.4.2

Multiply $5$ by $5$ .

$(45 z + 54 y) \cdot (30 z + 25 y)$

Step 2

Expand $(45 z + 54 y) (30 z + 25 y)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$45 z (30 z + 25 y) + 54 y (30 z + 25 y)$

Step 2.2

Apply the distributive property.

$45 z (30 z) + 45 z (25 y) + 54 y (30 z + 25 y)$

Step 2.3

Apply the distributive property.

$45 z (30 z) + 45 z (25 y) + 54 y (30 z) + 54 y (25 y)$

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.

$45 \cdot 30 z \cdot z + 45 z (25 y) + 54 y (30 z) + 54 y (25 y)$

Step 3.1.2

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

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Step 3.1.2.1

Move $z$ .

$45 \cdot 30 (z \cdot z) + 45 z (25 y) + 54 y (30 z) + 54 y (25 y)$

Step 3.1.2.2

Multiply $z$ by $z$ .

$45 \cdot 30 z^{2} + 45 z (25 y) + 54 y (30 z) + 54 y (25 y)$

Step 3.1.3

Multiply $45$ by $30$ .

$1350 z^{2} + 45 z (25 y) + 54 y (30 z) + 54 y (25 y)$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$1350 z^{2} + 45 \cdot 25 z y + 54 y (30 z) + 54 y (25 y)$

Step 3.1.5

Multiply $45$ by $25$ .

$1350 z^{2} + 1125 z y + 54 y (30 z) + 54 y (25 y)$

Step 3.1.6

Rewrite using the commutative property of multiplication.

$1350 z^{2} + 1125 z y + 54 \cdot 30 y z + 54 y (25 y)$

Step 3.1.7

Multiply $54$ by $30$ .

$1350 z^{2} + 1125 z y + 1620 y z + 54 y (25 y)$

Step 3.1.8

Rewrite using the commutative property of multiplication.

$1350 z^{2} + 1125 z y + 1620 y z + 54 \cdot 25 y \cdot y$

Step 3.1.9

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

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Step 3.1.9.1

Move $y$ .

$1350 z^{2} + 1125 z y + 1620 y z + 54 \cdot 25 (y \cdot y)$

Step 3.1.9.2

Multiply $y$ by $y$ .

$1350 z^{2} + 1125 z y + 1620 y z + 54 \cdot 25 y^{2}$

Step 3.1.10

Multiply $54$ by $25$ .

$1350 z^{2} + 1125 z y + 1620 y z + 1350 y^{2}$

Step 3.2

Add $1125 z y$ and $1620 y z$ .

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Step 3.2.1

Move $z$ .

$1350 z^{2} + 1125 y z + 1620 y z + 1350 y^{2}$

Step 3.2.2

Add $1125 y z$ and $1620 y z$ .

$1350 z^{2} + 2745 y z + 1350 y^{2}$

Step 4

Move $1350 z^{2}$ .

$2745 y z + 1350 y^{2} + 1350 z^{2}$

Step 5

Reorder $2745 y z$ and $1350 y^{2}$ .

$1350 y^{2} + 2745 y z + 1350 z^{2}$