Write in Standard Form 10(x-2)-5(x^2-7x)+x(3x+6)

$10 (x - 2) - 5 (x^{2} - 7 x) + x (3 x + 6)$

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

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

Simplify each term.

Apply the distributive property.

$10 x + 10 \cdot - 2 - 5 (x^{2} - 7 x) + x (3 x + 6)$

Multiply $10$ by $- 2$ .

$10 x - 20 - 5 (x^{2} - 7 x) + x (3 x + 6)$

Apply the distributive property.

$10 x - 20 - 5 x^{2} - 5 (- 7 x) + x (3 x + 6)$

Multiply $- 7$ by $- 5$ .

$10 x - 20 - 5 x^{2} + 35 x + x (3 x + 6)$

Apply the distributive property.

$10 x - 20 - 5 x^{2} + 35 x + x (3 x) + x \cdot 6$

Rewrite using the commutative property of multiplication.

$10 x - 20 - 5 x^{2} + 35 x + 3 x \cdot x + x \cdot 6$

Move $6$ to the left of $x$ .

$10 x - 20 - 5 x^{2} + 35 x + 3 x \cdot x + 6 \cdot x$

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

Move $x$ .

$10 x - 20 - 5 x^{2} + 35 x + 3 (x \cdot x) + 6 \cdot x$

Multiply $x$ by $x$ .

$10 x - 20 - 5 x^{2} + 35 x + 3 x^{2} + 6 \cdot x$

$10 x - 20 - 5 x^{2} + 35 x + 3 x^{2} + 6 x$

Simplify by adding terms.

Add $10 x$ and $35 x$ .

$45 x - 20 - 5 x^{2} + 3 x^{2} + 6 x$

Add $45 x$ and $6 x$ .

$- 20 - 5 x^{2} + 3 x^{2} + 51 x$

Add $- 5 x^{2}$ and $3 x^{2}$ .

$- 20 - 2 x^{2} + 51 x$

Move $- 20$ .

$- 2 x^{2} + 51 x - 20$