Write in Standard Form y=(4x+3)^2-24x

$y = {(4 x + 3)}^{2} - 24 x$

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

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

Simplify each term.

Rewrite ${(4 x + 3)}^{2}$ as $(4 x + 3) (4 x + 3)$ .

$y = (4 x + 3) (4 x + 3) - 24 x$

Expand $(4 x + 3) (4 x + 3)$ using the FOIL Method.

Apply the distributive property.

$y = 4 x (4 x + 3) + 3 (4 x + 3) - 24 x$

Apply the distributive property.

$y = 4 x (4 x) + 4 x \cdot 3 + 3 (4 x + 3) - 24 x$

Apply the distributive property.

$y = 4 x (4 x) + 4 x \cdot 3 + 3 (4 x) + 3 \cdot 3 - 24 x$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$y = 4 \cdot (4 x \cdot x) + 4 x \cdot 3 + 3 (4 x) + 3 \cdot 3 - 24 x$

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

Move $x$ .

$y = 4 \cdot (4 (x \cdot x)) + 4 x \cdot 3 + 3 (4 x) + 3 \cdot 3 - 24 x$

Multiply $x$ by $x$ .

$y = 4 \cdot (4 x^{2}) + 4 x \cdot 3 + 3 (4 x) + 3 \cdot 3 - 24 x$

Multiply $4$ by $4$ .

$y = 16 x^{2} + 4 x \cdot 3 + 3 (4 x) + 3 \cdot 3 - 24 x$

Multiply $3$ by $4$ .

$y = 16 x^{2} + 12 x + 3 (4 x) + 3 \cdot 3 - 24 x$

Multiply $4$ by $3$ .

$y = 16 x^{2} + 12 x + 12 x + 3 \cdot 3 - 24 x$

Multiply $3$ by $3$ .

$y = 16 x^{2} + 12 x + 12 x + 9 - 24 x$

Add $12 x$ and $12 x$ .

$y = 16 x^{2} + 24 x + 9 - 24 x$

Combine the opposite terms in $16 x^{2} + 24 x + 9 - 24 x$ .

Subtract $24 x$ from $24 x$ .

$y = 16 x^{2} + 0 + 9$

Add $16 x^{2}$ and $0$ .

$y = 16 x^{2} + 9$