This math topic focuses on simplifying algebraic expressions with polynomials involving variables exponentiated to high powers, then divided by an expression with a similar base but lesser exponent. Each problem presents an expression for simplification, paired with multiple-choice answers. The expressions typically involve subtracting or adding different powers of a variable, then dividing by one of the powers, challenging the student to simplify them to a simpler form using properties of exponents and basic algebraic skills. This set of problems is an advanced application of polynomial operations and exponent rules.

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Polynomial Algebra - Difference of Exponents (Variables) Divided by Second Exponent - Simplify Worksheet

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Polynomial Algebra - Difference of Exponents (Variables) Divided by Second Exponent - Simplify
1
What does this expression simplify to?
A LaTex expression showing \frac{d to the power of 2014 + d to the power of 2013 }{d to the power of 2013 }
a A LaTex expression showing d - 1
b A LaTex expression showing (d + 1) to the power of 2
c A LaTex expression showing (d + 1)(d - 1)
d A LaTex expression showing d + 1
2
What does this expression simplify to?
A LaTex expression showing \frac{y to the power of 2003 - y to the power of 2002 }{y to the power of 2002 }
a A LaTex expression showing y - 1
b A LaTex expression showing y + 1
c A LaTex expression showing (y + 1) to the power of 2
d A LaTex expression showing (y + 1)(y - 1)
3
What does this expression simplify to?
A LaTex expression showing \frac{m to the power of 2009 + m to the power of 2008 }{m to the power of 2008 }
a A LaTex expression showing m + 1
b A LaTex expression showing m - 1
c A LaTex expression showing (m + 1) to the power of 2
d A LaTex expression showing (m + 1)(m - 1)
4
What does this expression simplify to?
A LaTex expression showing \frac{r to the power of 2011 - r to the power of 2010 }{r to the power of 2010 }
a A LaTex expression showing (r + 1)(r - 1)
b A LaTex expression showing r - 1
c A LaTex expression showing (r + 1) to the power of 2
d A LaTex expression showing r + 1
5
What does this expression simplify to?
A LaTex expression showing \frac{p to the power of 2014 - p to the power of 2013 }{p to the power of 2013 }
a A LaTex expression showing p + 1
b A LaTex expression showing (p + 1) to the power of 2
c A LaTex expression showing p - 1
d A LaTex expression showing (p + 1)(p - 1)
6
What does this expression simplify to?
A LaTex expression showing \frac{m to the power of 2018 + m to the power of 2017 }{m to the power of 2017 }
a A LaTex expression showing (m + 1) to the power of 2
b A LaTex expression showing m - 1
c A LaTex expression showing m + 1
d A LaTex expression showing (m + 1)(m - 1)
7
What does this expression simplify to?
A LaTex expression showing \frac{r to the power of 2015 + r to the power of 2014 }{r to the power of 2014 }
a A LaTex expression showing (r + 1) to the power of 2
b A LaTex expression showing r - 1
c A LaTex expression showing (r + 1)(r - 1)
d A LaTex expression showing r + 1
8
What does this expression simplify to?
A LaTex expression showing \frac{r to the power of 2024 - r to the power of 2023 }{r to the power of 2023 }
a A LaTex expression showing r - 1
b A LaTex expression showing (r + 1) to the power of 2
c A LaTex expression showing r + 1
d A LaTex expression showing (r + 1)(r - 1)