Write in Standard Form (5y^2-2y+1)-(y^2+y+3)

$(5 y^{2} - 2 y + 1) - (y^{2} + y + 3)$

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.

$5 y^{2} - 2 y + 1 - y^{2} - y - 1 \cdot 3$

Multiply $- 1$ by $3$ .

$5 y^{2} - 2 y + 1 - y^{2} - y - 3$

Simplify by adding terms.

Subtract $y^{2}$ from $5 y^{2}$ .

$4 y^{2} - 2 y + 1 - y - 3$

Subtract $y$ from $- 2 y$ .

$4 y^{2} - 3 y + 1 - 3$

Subtract $3$ from $1$ .

$4 y^{2} - 3 y - 2$