Question

which represents the polynomial written in standard form?
$8x^2y^2 - 3x^3y + 4x^4 - 7xy^3$
$\bigcirc\\ 4x^4 - 3x^3y + 8x^2y^2 - 7xy^3$
$\bigcirc\\ 4x^4 - 7xy^3 - 3x^3y + 8x^2y^2$
$\bigcirc\\ 4x^4 + 8x^2y^2 - 3x^3y - 7xy^3$
$\bigcirc\\ -7xy^3 - 3x^3y + 8x^2y^2 + 4x^4$

Explanation:

Step1: Define standard polynomial form

Standard form for a multivariable polynomial orders terms by descending total degree (sum of exponents of variables in each term).

Step2: Calculate term degrees

• For $4x^4$: degree = $4$
• For $-3x^3y$: degree = $3+1=4$
• For $8x^2y^2$: degree = $2+2=4$
• For $-7xy^3$: degree = $1+3=4$

When degrees are equal, order by descending exponent of $x$:

• $4x^4$ ($x^4$) > $-3x^3y$ ($x^3$) > $8x^2y^2$ ($x^2$) > $-7xy^3$ ($x^1$)

Answer:

$4x^4 - 3x^3y + 8x^2y^2 - 7xy^3$ (first option)