Basic Math Examples

$7 z (5 z - y) (5 z - y)$

Step 1

Simplify terms.

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Step 1.1

Apply the distributive property.

$(7 z (5 z) + 7 z (- y)) (5 z - y)$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$(7 \cdot 5 z \cdot z + 7 z (- y)) (5 z - y)$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$(7 \cdot 5 z \cdot z + 7 \cdot - 1 z y) (5 z - y)$

Step 1.3

Simplify each term.

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Step 1.3.1

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

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Step 1.3.1.1

Move $z$ .

$(7 \cdot 5 (z \cdot z) + 7 \cdot - 1 z y) (5 z - y)$

Step 1.3.1.2

Multiply $z$ by $z$ .

$(7 \cdot 5 z^{2} + 7 \cdot - 1 z y) (5 z - y)$

Step 1.3.2

Multiply $7$ by $5$ .

$(35 z^{2} + 7 \cdot - 1 z y) (5 z - y)$

Step 1.3.3

Multiply $7$ by $- 1$ .

$(35 z^{2} - 7 z y) (5 z - y)$

Step 2

Expand $(35 z^{2} - 7 z y) (5 z - y)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$35 z^{2} (5 z - y) - 7 z y (5 z - y)$

Step 2.2

Apply the distributive property.

$35 z^{2} (5 z) + 35 z^{2} (- y) - 7 z y (5 z - y)$

Step 2.3

Apply the distributive property.

$35 z^{2} (5 z) + 35 z^{2} (- y) - 7 z y (5 z) - 7 z y (- y)$

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.

$35 \cdot 5 z^{2} z + 35 z^{2} (- y) - 7 z y (5 z) - 7 z y (- y)$

Step 3.1.2

Multiply $z^{2}$ by $z$ by adding the exponents.

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Step 3.1.2.1

Move $z$ .

$35 \cdot 5 (z \cdot z^{2}) + 35 z^{2} (- y) - 7 z y (5 z) - 7 z y (- y)$

Step 3.1.2.2

Multiply $z$ by $z^{2}$ .

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Step 3.1.2.2.1

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

$35 \cdot 5 (z^{1} z^{2}) + 35 z^{2} (- y) - 7 z y (5 z) - 7 z y (- y)$

Step 3.1.2.2.2

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

$35 \cdot 5 z^{1 + 2} + 35 z^{2} (- y) - 7 z y (5 z) - 7 z y (- y)$

Step 3.1.2.3

Add $1$ and $2$ .

$35 \cdot 5 z^{3} + 35 z^{2} (- y) - 7 z y (5 z) - 7 z y (- y)$

Step 3.1.3

Multiply $35$ by $5$ .

$175 z^{3} + 35 z^{2} (- y) - 7 z y (5 z) - 7 z y (- y)$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$175 z^{3} + 35 \cdot - 1 z^{2} y - 7 z y (5 z) - 7 z y (- y)$

Step 3.1.5

Multiply $35$ by $- 1$ .

$175 z^{3} - 35 z^{2} y - 7 z y (5 z) - 7 z y (- y)$

Step 3.1.6

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

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Step 3.1.6.1

Move $z$ .

$175 z^{3} - 35 z^{2} y - 7 (z \cdot z) y \cdot 5 - 7 z y (- y)$

Step 3.1.6.2

Multiply $z$ by $z$ .

$175 z^{3} - 35 z^{2} y - 7 z^{2} y \cdot 5 - 7 z y (- y)$

Step 3.1.7

Multiply $5$ by $- 7$ .

$175 z^{3} - 35 z^{2} y - 35 z^{2} y - 7 z y (- y)$

Step 3.1.8

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

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Step 3.1.8.1

Move $y$ .

$175 z^{3} - 35 z^{2} y - 35 z^{2} y - 7 z (y \cdot y) \cdot - 1$

Step 3.1.8.2

Multiply $y$ by $y$ .

$175 z^{3} - 35 z^{2} y - 35 z^{2} y - 7 z y^{2} \cdot - 1$

Step 3.1.9

Multiply $- 1$ by $- 7$ .

$175 z^{3} - 35 z^{2} y - 35 z^{2} y + 7 z y^{2}$

Step 3.2

Subtract $35 z^{2} y$ from $- 35 z^{2} y$ .

$175 z^{3} - 70 z^{2} y + 7 z y^{2}$