Write in Standard Form 6z^2(7z^2+3z-2)

$6 z^{2} (7 z^{2} + 3 z - 2)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Apply the distributive property.

$6 z^{2} (7 z^{2}) + 6 z^{2} (3 z) + 6 z^{2} \cdot - 2$

Step 3

Simplify.

Rewrite using the commutative property of multiplication.

$6 \cdot 7 z^{2} z^{2} + 6 z^{2} (3 z) + 6 z^{2} \cdot - 2$

Rewrite using the commutative property of multiplication.

$6 \cdot 7 z^{2} z^{2} + 6 \cdot 3 z^{2} z + 6 z^{2} \cdot - 2$

Multiply $- 2$ by $6$ .

$6 \cdot 7 z^{2} z^{2} + 6 \cdot 3 z^{2} z - 12 z^{2}$

Step 4

Simplify each term.

Multiply $z^{2}$ by $z^{2}$ by adding the exponents.

Move $z^{2}$ .

$6 \cdot 7 (z^{2} z^{2}) + 6 \cdot 3 z^{2} z - 12 z^{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$6 \cdot 7 z^{2 + 2} + 6 \cdot 3 z^{2} z - 12 z^{2}$

Add $2$ and $2$ .

$6 \cdot 7 z^{4} + 6 \cdot 3 z^{2} z - 12 z^{2}$

Multiply $6$ by $7$ .

$42 z^{4} + 6 \cdot 3 z^{2} z - 12 z^{2}$

Multiply $z^{2}$ by $z$ by adding the exponents.

Move $z$ .

$42 z^{4} + 6 \cdot 3 (z \cdot z^{2}) - 12 z^{2}$

Multiply $z$ by $z^{2}$ .

Raise $z$ to the power of $1$ .

$42 z^{4} + 6 \cdot 3 (z^{1} z^{2}) - 12 z^{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$42 z^{4} + 6 \cdot 3 z^{1 + 2} - 12 z^{2}$

Add $1$ and $2$ .

$42 z^{4} + 6 \cdot 3 z^{3} - 12 z^{2}$

Multiply $6$ by $3$ .

$42 z^{4} + 18 z^{3} - 12 z^{2}$