Write in Standard Form y=4(3x+1)(5x-6)

$y = 4 (3 x + 1) (5 x - 6)$

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

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

Simplify by multiplying through.

Apply the distributive property.

$y = (4 (3 x) + 4 \cdot 1) (5 x - 6)$

Multiply.

Multiply $3$ by $4$ .

$y = (12 x + 4 \cdot 1) (5 x - 6)$

Multiply $4$ by $1$ .

$y = (12 x + 4) (5 x - 6)$

Expand $(12 x + 4) (5 x - 6)$ using the FOIL Method.

Apply the distributive property.

$y = 12 x (5 x - 6) + 4 (5 x - 6)$

Apply the distributive property.

$y = 12 x (5 x) + 12 x \cdot - 6 + 4 (5 x - 6)$

Apply the distributive property.

$y = 12 x (5 x) + 12 x \cdot - 6 + 4 (5 x) + 4 \cdot - 6$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$y = 12 \cdot (5 x \cdot x) + 12 x \cdot - 6 + 4 (5 x) + 4 \cdot - 6$

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

Move $x$ .

$y = 12 \cdot (5 (x \cdot x)) + 12 x \cdot - 6 + 4 (5 x) + 4 \cdot - 6$

Multiply $x$ by $x$ .

$y = 12 \cdot (5 x^{2}) + 12 x \cdot - 6 + 4 (5 x) + 4 \cdot - 6$

Multiply $12$ by $5$ .

$y = 60 x^{2} + 12 x \cdot - 6 + 4 (5 x) + 4 \cdot - 6$

Multiply $- 6$ by $12$ .

$y = 60 x^{2} - 72 x + 4 (5 x) + 4 \cdot - 6$

Multiply $5$ by $4$ .

$y = 60 x^{2} - 72 x + 20 x + 4 \cdot - 6$

Multiply $4$ by $- 6$ .

$y = 60 x^{2} - 72 x + 20 x - 24$

Add $- 72 x$ and $20 x$ .

$y = 60 x^{2} - 52 x - 24$