Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(4 z - 3)}^{2}$ as $(4 z - 3) (4 z - 3)$ .

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

Step 1.2

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

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Apply the distributive property.

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

Step 1.2.3

Apply the distributive property.

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

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Rewrite using the commutative property of multiplication.

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

Step 1.3.1.2

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

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Step 1.3.1.2.1

Move $z$ .

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

Step 1.3.1.2.2

Multiply $z$ by $z$ .

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

Step 1.3.1.3

Multiply $4$ by $4$ .

$16 z^{2} + 4 z \cdot - 3 - 3 (4 z) - 3 \cdot - 3 - 2 (4 + 3 z (5 z - 3))$

Step 1.3.1.4

Multiply $- 3$ by $4$ .

$16 z^{2} - 12 z - 3 (4 z) - 3 \cdot - 3 - 2 (4 + 3 z (5 z - 3))$

Step 1.3.1.5

Multiply $4$ by $- 3$ .

$16 z^{2} - 12 z - 12 z - 3 \cdot - 3 - 2 (4 + 3 z (5 z - 3))$

Step 1.3.1.6

Multiply $- 3$ by $- 3$ .

$16 z^{2} - 12 z - 12 z + 9 - 2 (4 + 3 z (5 z - 3))$

Step 1.3.2

Subtract $12 z$ from $- 12 z$ .

$16 z^{2} - 24 z + 9 - 2 (4 + 3 z (5 z - 3))$

Step 1.4

Simplify each term.

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Step 1.4.1

Apply the distributive property.

$16 z^{2} - 24 z + 9 - 2 (4 + 3 z (5 z) + 3 z \cdot - 3)$

Step 1.4.2

Rewrite using the commutative property of multiplication.

$16 z^{2} - 24 z + 9 - 2 (4 + 3 \cdot 5 z \cdot z + 3 z \cdot - 3)$

Step 1.4.3

Multiply $- 3$ by $3$ .

$16 z^{2} - 24 z + 9 - 2 (4 + 3 \cdot 5 z \cdot z - 9 z)$

Step 1.4.4

Simplify each term.

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Step 1.4.4.1

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

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Step 1.4.4.1.1

Move $z$ .

$16 z^{2} - 24 z + 9 - 2 (4 + 3 \cdot 5 (z \cdot z) - 9 z)$

Step 1.4.4.1.2

Multiply $z$ by $z$ .

$16 z^{2} - 24 z + 9 - 2 (4 + 3 \cdot 5 z^{2} - 9 z)$

Step 1.4.4.2

Multiply $3$ by $5$ .

$16 z^{2} - 24 z + 9 - 2 (4 + 15 z^{2} - 9 z)$

Step 1.5

Apply the distributive property.

$16 z^{2} - 24 z + 9 - 2 \cdot 4 - 2 (15 z^{2}) - 2 (- 9 z)$

Step 1.6

Simplify.

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Step 1.6.1

Multiply $- 2$ by $4$ .

$16 z^{2} - 24 z + 9 - 8 - 2 (15 z^{2}) - 2 (- 9 z)$

Step 1.6.2

Multiply $15$ by $- 2$ .

$16 z^{2} - 24 z + 9 - 8 - 30 z^{2} - 2 (- 9 z)$

Step 1.6.3

Multiply $- 9$ by $- 2$ .

$16 z^{2} - 24 z + 9 - 8 - 30 z^{2} + 18 z$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $30 z^{2}$ from $16 z^{2}$ .

$- 14 z^{2} - 24 z + 9 - 8 + 18 z$

Step 2.2

Add $- 24 z$ and $18 z$ .

$- 14 z^{2} - 6 z + 9 - 8$

Step 2.3

Subtract $8$ from $9$ .

$- 14 z^{2} - 6 z + 1$