This math topic focuses on simplifying expressions involving exponents and polynomials. Specifically, it explores the simplification of expressions where the difference or sum of powers of a variable is divided by one of those exponents. For instance, tasks ask students to simplify expressions like \((c^{132} - c^{131})/c^{131}\) and similar constructs with other variables such as \(m\), \(r\), \(n\), \(z\), and \(y\). The problems are designed to strengthen understanding of exponent rules, factoring, and polynomial simplification at an advanced level within the broader unit of Polynomials and Quadratics.

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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{n to the power of 112 + n to the power of 111 }{n to the power of 111 }
a A LaTex expression showing (n + 1)(n - 1)
b A LaTex expression showing (n + 1) to the power of 2
c A LaTex expression showing n + 1
d A LaTex expression showing n - 1
2
What does this expression simplify to?
A LaTex expression showing \frac{y to the power of 290 + y to the power of 289 }{y to the power of 289 }
a A LaTex expression showing (y + 1) to the power of 2
b A LaTex expression showing y + 1
c A LaTex expression showing (y + 1)(y - 1)
d A LaTex expression showing y - 1
3
What does this expression simplify to?
A LaTex expression showing \frac{x to the power of 162 + x to the power of 161 }{x to the power of 161 }
a A LaTex expression showing x - 1
b A LaTex expression showing x + 1
c A LaTex expression showing (x + 1) to the power of 2
d A LaTex expression showing (x + 1)(x - 1)
4
What does this expression simplify to?
A LaTex expression showing \frac{d to the power of 412 - d to the power of 411 }{d to the power of 411 }
a A LaTex expression showing d - 1
b A LaTex expression showing d + 1
c A LaTex expression showing (d + 1)(d - 1)
d A LaTex expression showing (d + 1) to the power of 2
5
What does this expression simplify to?
A LaTex expression showing \frac{c to the power of 278 - c to the power of 277 }{c to the power of 277 }
a A LaTex expression showing c - 1
b A LaTex expression showing (c + 1)(c - 1)
c A LaTex expression showing (c + 1) to the power of 2
d A LaTex expression showing c + 1
6
What does this expression simplify to?
A LaTex expression showing \frac{m to the power of 245 - m to the power of 244 }{m to the power of 244 }
a A LaTex expression showing (m + 1)(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
7
What does this expression simplify to?
A LaTex expression showing \frac{c to the power of 434 - c to the power of 433 }{c to the power of 433 }
a A LaTex expression showing c + 1
b A LaTex expression showing c - 1
c A LaTex expression showing (c + 1)(c - 1)
d A LaTex expression showing (c + 1) to the power of 2
8
What does this expression simplify to?
A LaTex expression showing \frac{d to the power of 188 - d to the power of 187 }{d to the power of 187 }
a A LaTex expression showing d + 1
b A LaTex expression showing (d + 1)(d - 1)
c A LaTex expression showing d - 1
d A LaTex expression showing (d + 1) to the power of 2