<h3>Given</h3>
–5x3y3 + 8x4y2 – xy5 – 2x2y4 + 8x6 + 3x2y4 – 6xy5
<h3>Find</h3>
Which of the following represents the expression written in standard form:
–7xy5 + 5x2y4 – 5x3y3 + 8x4y2 + 8x6
5xy5 + 8x4y2 + x2y4 – 5x3y3 + 8x6
8x6 + 5xy5 + 8x4y2 + x2y4 – 5x3y3
8x6 + 8x4y2 – 5x3y3 + x2y4 – 7xy5
<h3>Solution</h3>
The variables are x and y. All terms have degree 6, so we can choose to write them in order of decreasing powers of x or of decreasing powers of y.
The terms tha can be combined are those involving xy⁵ and x²y⁴. Combining those terms, we have xy⁵(-1-6) = -7xy⁵, and x²y⁴(-2+3) = x²y⁴.
The first offered choice has the powers of y in decreasing order, but it has an incorrect coefficient for x²y⁴. The second and third offered choices have no consistent ordering of powers.
The best choice is the last one:
... 8x⁶ +8x⁴y² -5x³y³ +x²y⁴ -7xy⁵
