Basic Math Examples

$(- 7 z + y) (4 z - 5 y)$

Step 1

Expand $(- 7 z + y) (4 z - 5 y)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$- 7 z (4 z - 5 y) + y (4 z - 5 y)$

Step 1.2

Apply the distributive property.

$- 7 z (4 z) - 7 z (- 5 y) + y (4 z - 5 y)$

Step 1.3

Apply the distributive property.

$- 7 z (4 z) - 7 z (- 5 y) + y (4 z) + y (- 5 y)$

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.

$- 7 \cdot 4 z \cdot z - 7 z (- 5 y) + y (4 z) + y (- 5 y)$

Step 2.1.2

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

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Step 2.1.2.1

Move $z$ .

$- 7 \cdot 4 (z \cdot z) - 7 z (- 5 y) + y (4 z) + y (- 5 y)$

Step 2.1.2.2

Multiply $z$ by $z$ .

$- 7 \cdot 4 z^{2} - 7 z (- 5 y) + y (4 z) + y (- 5 y)$

Step 2.1.3

Multiply $- 7$ by $4$ .

$- 28 z^{2} - 7 z (- 5 y) + y (4 z) + y (- 5 y)$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$- 28 z^{2} - 7 \cdot - 5 z y + y (4 z) + y (- 5 y)$

Step 2.1.5

Multiply $- 7$ by $- 5$ .

$- 28 z^{2} + 35 z y + y (4 z) + y (- 5 y)$

Step 2.1.6

Rewrite using the commutative property of multiplication.

$- 28 z^{2} + 35 z y + 4 y z + y (- 5 y)$

Step 2.1.7

Rewrite using the commutative property of multiplication.

$- 28 z^{2} + 35 z y + 4 y z - 5 y \cdot y$

Step 2.1.8

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

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Step 2.1.8.1

Move $y$ .

$- 28 z^{2} + 35 z y + 4 y z - 5 (y \cdot y)$

Step 2.1.8.2

Multiply $y$ by $y$ .

$- 28 z^{2} + 35 z y + 4 y z - 5 y^{2}$

Step 2.2

Add $35 z y$ and $4 y z$ .

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Step 2.2.1

Move $z$ .

$- 28 z^{2} + 35 y z + 4 y z - 5 y^{2}$

Step 2.2.2

Add $35 y z$ and $4 y z$ .

$- 28 z^{2} + 39 y z - 5 y^{2}$

Step 3

Move $- 28 z^{2}$ .

$39 y z - 5 y^{2} - 28 z^{2}$

Step 4

Reorder $39 y z$ and $- 5 y^{2}$ .

$- 5 y^{2} + 39 y z - 28 z^{2}$