Calculus Examples

$(4 z - 5) (3 z - 2) - (3 z - 9) (3 z - 2)$

Step 1

Simplify each term.

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Step 1.1

Expand $(4 z - 5) (3 z - 2)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$4 z (3 z - 2) - 5 (3 z - 2) - (3 z - 9) (3 z - 2)$

Step 1.1.2

Apply the distributive property.

$4 z (3 z) + 4 z \cdot - 2 - 5 (3 z - 2) - (3 z - 9) (3 z - 2)$

Step 1.1.3

Apply the distributive property.

$4 z (3 z) + 4 z \cdot - 2 - 5 (3 z) - 5 \cdot - 2 - (3 z - 9) (3 z - 2)$

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Rewrite using the commutative property of multiplication.

$4 \cdot 3 z \cdot z + 4 z \cdot - 2 - 5 (3 z) - 5 \cdot - 2 - (3 z - 9) (3 z - 2)$

Step 1.2.1.2

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

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Step 1.2.1.2.1

Move $z$ .

$4 \cdot 3 (z \cdot z) + 4 z \cdot - 2 - 5 (3 z) - 5 \cdot - 2 - (3 z - 9) (3 z - 2)$

Step 1.2.1.2.2

Multiply $z$ by $z$ .

$4 \cdot 3 z^{2} + 4 z \cdot - 2 - 5 (3 z) - 5 \cdot - 2 - (3 z - 9) (3 z - 2)$

Step 1.2.1.3

Multiply $4$ by $3$ .

$12 z^{2} + 4 z \cdot - 2 - 5 (3 z) - 5 \cdot - 2 - (3 z - 9) (3 z - 2)$

Step 1.2.1.4

Multiply $- 2$ by $4$ .

$12 z^{2} - 8 z - 5 (3 z) - 5 \cdot - 2 - (3 z - 9) (3 z - 2)$

Step 1.2.1.5

Multiply $3$ by $- 5$ .

$12 z^{2} - 8 z - 15 z - 5 \cdot - 2 - (3 z - 9) (3 z - 2)$

Step 1.2.1.6

Multiply $- 5$ by $- 2$ .

$12 z^{2} - 8 z - 15 z + 10 - (3 z - 9) (3 z - 2)$

Step 1.2.2

Subtract $15 z$ from $- 8 z$ .

$12 z^{2} - 23 z + 10 - (3 z - 9) (3 z - 2)$

Step 1.3

Apply the distributive property.

$12 z^{2} - 23 z + 10 + (- (3 z) - - 9) (3 z - 2)$

Step 1.4

Multiply $3$ by $- 1$ .

$12 z^{2} - 23 z + 10 + (- 3 z - - 9) (3 z - 2)$

Step 1.5

Multiply $- 1$ by $- 9$ .

$12 z^{2} - 23 z + 10 + (- 3 z + 9) (3 z - 2)$

Step 1.6

Expand $(- 3 z + 9) (3 z - 2)$ using the FOIL Method.

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Step 1.6.1

Apply the distributive property.

$12 z^{2} - 23 z + 10 - 3 z (3 z - 2) + 9 (3 z - 2)$

Step 1.6.2

Apply the distributive property.

$12 z^{2} - 23 z + 10 - 3 z (3 z) - 3 z \cdot - 2 + 9 (3 z - 2)$

Step 1.6.3

Apply the distributive property.

$12 z^{2} - 23 z + 10 - 3 z (3 z) - 3 z \cdot - 2 + 9 (3 z) + 9 \cdot - 2$

Step 1.7

Simplify and combine like terms.

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Step 1.7.1

Simplify each term.

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Step 1.7.1.1

Rewrite using the commutative property of multiplication.

$12 z^{2} - 23 z + 10 - 3 \cdot 3 z \cdot z - 3 z \cdot - 2 + 9 (3 z) + 9 \cdot - 2$

Step 1.7.1.2

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

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Step 1.7.1.2.1

Move $z$ .

$12 z^{2} - 23 z + 10 - 3 \cdot 3 (z \cdot z) - 3 z \cdot - 2 + 9 (3 z) + 9 \cdot - 2$

Step 1.7.1.2.2

Multiply $z$ by $z$ .

$12 z^{2} - 23 z + 10 - 3 \cdot 3 z^{2} - 3 z \cdot - 2 + 9 (3 z) + 9 \cdot - 2$

Step 1.7.1.3

Multiply $- 3$ by $3$ .

$12 z^{2} - 23 z + 10 - 9 z^{2} - 3 z \cdot - 2 + 9 (3 z) + 9 \cdot - 2$

Step 1.7.1.4

Multiply $- 2$ by $- 3$ .

$12 z^{2} - 23 z + 10 - 9 z^{2} + 6 z + 9 (3 z) + 9 \cdot - 2$

Step 1.7.1.5

Multiply $3$ by $9$ .

$12 z^{2} - 23 z + 10 - 9 z^{2} + 6 z + 27 z + 9 \cdot - 2$

Step 1.7.1.6

Multiply $9$ by $- 2$ .

$12 z^{2} - 23 z + 10 - 9 z^{2} + 6 z + 27 z - 18$

Step 1.7.2

Add $6 z$ and $27 z$ .

$12 z^{2} - 23 z + 10 - 9 z^{2} + 33 z - 18$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $9 z^{2}$ from $12 z^{2}$ .

$3 z^{2} - 23 z + 10 + 33 z - 18$

Step 2.2

Add $- 23 z$ and $33 z$ .

$3 z^{2} + 10 z + 10 - 18$

Step 2.3

Subtract $18$ from $10$ .

$3 z^{2} + 10 z - 8$