Write in Standard Form y=(3x+1)(2x-7)

$y = (3 x + 1) (2 x - 7)$

Step 1

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

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

Step 2

Expand $(3 x + 1) (2 x - 7)$ using the FOIL Method.

Apply the distributive property.

$y = 3 x (2 x - 7) + 1 (2 x - 7)$

Apply the distributive property.

$y = 3 x (2 x) + 3 x \cdot - 7 + 1 (2 x - 7)$

Apply the distributive property.

$y = 3 x (2 x) + 3 x \cdot - 7 + 1 (2 x) + 1 \cdot - 7$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$y = 3 \cdot (2 x \cdot x) + 3 x \cdot - 7 + 1 (2 x) + 1 \cdot - 7$

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

Move $x$ .

$y = 3 \cdot (2 (x \cdot x)) + 3 x \cdot - 7 + 1 (2 x) + 1 \cdot - 7$

Multiply $x$ by $x$ .

$y = 3 \cdot (2 x^{2}) + 3 x \cdot - 7 + 1 (2 x) + 1 \cdot - 7$

Multiply $3$ by $2$ .

$y = 6 x^{2} + 3 x \cdot - 7 + 1 (2 x) + 1 \cdot - 7$

Multiply $- 7$ by $3$ .

$y = 6 x^{2} - 21 x + 1 (2 x) + 1 \cdot - 7$

Multiply $2 x$ by $1$ .

$y = 6 x^{2} - 21 x + 2 x + 1 \cdot - 7$

Multiply $- 7$ by $1$ .

$y = 6 x^{2} - 21 x + 2 x - 7$

Add $- 21 x$ and $2 x$ .

$y = 6 x^{2} - 19 x - 7$

Step 4