Write in Standard Form (5x^2+6x-2)+4x(3x-7)

$(5 x^{2} + 6 x - 2) + 4 x (3 x - 7)$

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.

$5 x^{2} + 6 x - 2 + 4 x (3 x) + 4 x \cdot - 7$

Rewrite using the commutative property of multiplication.

$5 x^{2} + 6 x - 2 + 4 \cdot 3 x \cdot x + 4 x \cdot - 7$

Multiply $- 7$ by $4$ .

$5 x^{2} + 6 x - 2 + 4 \cdot 3 x \cdot x - 28 x$

Simplify each term.

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

Move $x$ .

$5 x^{2} + 6 x - 2 + 4 \cdot 3 (x \cdot x) - 28 x$

Multiply $x$ by $x$ .

$5 x^{2} + 6 x - 2 + 4 \cdot 3 x^{2} - 28 x$

Multiply $4$ by $3$ .

$5 x^{2} + 6 x - 2 + 12 x^{2} - 28 x$

Simplify by adding terms.

Add $5 x^{2}$ and $12 x^{2}$ .

$17 x^{2} + 6 x - 2 - 28 x$

Subtract $28 x$ from $6 x$ .

$17 x^{2} - 22 x - 2$