Basic Math Examples

$(7 y - 3 z) (7 y + 3 z)$

Step 1

Expand $(7 y - 3 z) (7 y + 3 z)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$7 y (7 y + 3 z) - 3 z (7 y + 3 z)$

Step 1.2

Apply the distributive property.

$7 y (7 y) + 7 y (3 z) - 3 z (7 y + 3 z)$

Step 1.3

Apply the distributive property.

$7 y (7 y) + 7 y (3 z) - 3 z (7 y) - 3 z (3 z)$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $7 y (7 y) + 7 y (3 z) - 3 z (7 y) - 3 z (3 z)$ .

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Step 2.1.1

Reorder the factors in the terms $7 y (3 z)$ and $- 3 z (7 y)$ .

$7 y (7 y) + 3 \cdot 7 y z - 3 \cdot 7 y z - 3 z (3 z)$

Step 2.1.2

Subtract $3 \cdot 7 y z$ from $3 \cdot 7 y z$ .

$7 y (7 y) + 0 - 3 z (3 z)$

Step 2.1.3

Add $7 y (7 y)$ and $0$ .

$7 y (7 y) - 3 z (3 z)$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$7 \cdot 7 y \cdot y - 3 z (3 z)$

Step 2.2.2

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

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Step 2.2.2.1

Move $y$ .

$7 \cdot 7 (y \cdot y) - 3 z (3 z)$

Step 2.2.2.2

Multiply $y$ by $y$ .

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

Step 2.2.3

Multiply $7$ by $7$ .

$49 y^{2} - 3 z (3 z)$

Step 2.2.4

Rewrite using the commutative property of multiplication.

$49 y^{2} - 3 \cdot 3 z \cdot z$

Step 2.2.5

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

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Step 2.2.5.1

Move $z$ .

$49 y^{2} - 3 \cdot 3 (z \cdot z)$

Step 2.2.5.2

Multiply $z$ by $z$ .

$49 y^{2} - 3 \cdot 3 z^{2}$

Step 2.2.6

Multiply $- 3$ by $3$ .

$49 y^{2} - 9 z^{2}$