Write in Standard Form -2x(6x^4-7x^2+x-5)

$- 2 x (6 x^{4} - 7 x^{2} + x - 5)$

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.

$- 2 x (6 x^{4}) - 2 x (- 7 x^{2}) - 2 x \cdot x - 2 x \cdot - 5$

Step 3

Simplify.

Rewrite using the commutative property of multiplication.

$- 2 \cdot 6 x \cdot x^{4} - 2 x (- 7 x^{2}) - 2 x \cdot x - 2 x \cdot - 5$

Rewrite using the commutative property of multiplication.

$- 2 \cdot 6 x \cdot x^{4} - 2 \cdot - 7 x \cdot x^{2} - 2 x \cdot x - 2 x \cdot - 5$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$- 2 \cdot 6 x \cdot x^{4} - 2 \cdot - 7 x \cdot x^{2} - 2 (x \cdot x) - 2 x \cdot - 5$

Multiply $x$ by $x$ .

$- 2 \cdot 6 x \cdot x^{4} - 2 \cdot - 7 x \cdot x^{2} - 2 x^{2} - 2 x \cdot - 5$

Multiply $- 5$ by $- 2$ .

$- 2 \cdot 6 x \cdot x^{4} - 2 \cdot - 7 x \cdot x^{2} - 2 x^{2} + 10 x$

Step 4

Simplify each term.

Multiply $x$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$- 2 \cdot 6 (x^{4} x) - 2 \cdot - 7 x \cdot x^{2} - 2 x^{2} + 10 x$

Multiply $x^{4}$ by $x$ .

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

$- 2 \cdot 6 (x^{4} x^{1}) - 2 \cdot - 7 x \cdot x^{2} - 2 x^{2} + 10 x$

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

$- 2 \cdot 6 x^{4 + 1} - 2 \cdot - 7 x \cdot x^{2} - 2 x^{2} + 10 x$

Add $4$ and $1$ .

$- 2 \cdot 6 x^{5} - 2 \cdot - 7 x \cdot x^{2} - 2 x^{2} + 10 x$

Multiply $- 2$ by $6$ .

$- 12 x^{5} - 2 \cdot - 7 x \cdot x^{2} - 2 x^{2} + 10 x$

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

Move $x^{2}$ .

$- 12 x^{5} - 2 \cdot - 7 (x^{2} x) - 2 x^{2} + 10 x$

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

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

$- 12 x^{5} - 2 \cdot - 7 (x^{2} x^{1}) - 2 x^{2} + 10 x$

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

$- 12 x^{5} - 2 \cdot - 7 x^{2 + 1} - 2 x^{2} + 10 x$

Add $2$ and $1$ .

$- 12 x^{5} - 2 \cdot - 7 x^{3} - 2 x^{2} + 10 x$

Multiply $- 2$ by $- 7$ .

$- 12 x^{5} + 14 x^{3} - 2 x^{2} + 10 x$

Write in Standard Form -2x(6x^4-7x^2+x-5)

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