Basic Math Examples

$(6 z + 7 y) (6 z - 7)$

Step 1

Expand $(6 z + 7 y) (6 z - 7)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$6 z (6 z - 7) + 7 y (6 z - 7)$

Step 1.2

Apply the distributive property.

$6 z (6 z) + 6 z \cdot - 7 + 7 y (6 z - 7)$

Step 1.3

Apply the distributive property.

$6 z (6 z) + 6 z \cdot - 7 + 7 y (6 z) + 7 y \cdot - 7$

Step 2

Simplify 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.

$6 \cdot 6 z \cdot z + 6 z \cdot - 7 + 7 y (6 z) + 7 y \cdot - 7$

Step 2.1.2

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

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Step 2.1.2.1

Move $z$ .

$6 \cdot 6 (z \cdot z) + 6 z \cdot - 7 + 7 y (6 z) + 7 y \cdot - 7$

Step 2.1.2.2

Multiply $z$ by $z$ .

$6 \cdot 6 z^{2} + 6 z \cdot - 7 + 7 y (6 z) + 7 y \cdot - 7$

Step 2.1.3

Multiply $6$ by $6$ .

$36 z^{2} + 6 z \cdot - 7 + 7 y (6 z) + 7 y \cdot - 7$

Step 2.1.4

Multiply $- 7$ by $6$ .

$36 z^{2} - 42 z + 7 y (6 z) + 7 y \cdot - 7$

Step 2.1.5

Rewrite using the commutative property of multiplication.

$36 z^{2} - 42 z + 7 \cdot 6 y z + 7 y \cdot - 7$

Step 2.1.6

Multiply $7$ by $6$ .

$36 z^{2} - 42 z + 42 y z + 7 y \cdot - 7$

Step 2.1.7

Multiply $- 7$ by $7$ .

$36 z^{2} - 42 z + 42 y z - 49 y$

Step 2.2

Simplify the expression.

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Step 2.2.1

Move $- 42 z$ .

$36 z^{2} + 42 y z - 49 y - 42 z$

Step 2.2.2

Reorder $36 z^{2}$ and $42 y z$ .

$42 y z + 36 z^{2} - 49 y - 42 z$