This math topic involves simplifying polynomial expressions with differences of variables raised to different powers, divided by a variable to a lower power. Each problem presents a fraction where the numerator contains the difference between two terms with exponentials, which is then divided by another exponential term in the denominator. The learner is tasked with simplifying these expressions to their most reduced form, testing their understanding of polynomial algebra within the context of Advanced 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{d to the power of 4 - d to the power of 3 }{d to the power of 3 }
a A LaTex expression showing (d + 1)(d - 1)
b A LaTex expression showing d - 1
c A LaTex expression showing (d + 1) to the power of 2
d A LaTex expression showing d + 1
2
What does this expression simplify to?
A LaTex expression showing \frac{p to the power of 5 - p to the power of 4 }{p to the power of 4 }
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)(p - 1)
d A LaTex expression showing p + 1
3
What does this expression simplify to?
A LaTex expression showing \frac{y to the power of 4 + y to the power of 3 }{y to the power of 3 }
a A LaTex expression showing y + 1
b A LaTex expression showing (y + 1) to the power of 2
c A LaTex expression showing y - 1
d A LaTex expression showing (y + 1)(y - 1)
4
What does this expression simplify to?
A LaTex expression showing \frac{y to the power of 4 - y to the power of 3 }{y to the power of 3 }
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
d A LaTex expression showing (y + 1)(y - 1)
5
What does this expression simplify to?
A LaTex expression showing \frac{z to the power of 5 - z to the power of 4 }{z to the power of 4 }
a A LaTex expression showing z + 1
b A LaTex expression showing z - 1
c A LaTex expression showing (z + 1) to the power of 2
d A LaTex expression showing (z + 1)(z - 1)
6
What does this expression simplify to?
A LaTex expression showing \frac{z to the power of 2 - z to the power of 1 }{z to the power of 1 }
a A LaTex expression showing z - 1
b A LaTex expression showing (z + 1) to the power of 2
c A LaTex expression showing z + 1
d A LaTex expression showing (z + 1)(z - 1)
7
What does this expression simplify to?
A LaTex expression showing \frac{y to the power of 5 - y to the power of 4 }{y to the power of 4 }
a A LaTex expression showing y - 1
b A LaTex expression showing y + 1
c A LaTex expression showing (y + 1)(y - 1)
d A LaTex expression showing (y + 1) to the power of 2
8
What does this expression simplify to?
A LaTex expression showing \frac{n to the power of 2 - n to the power of 1 }{n to the power of 1 }
a A LaTex expression showing n - 1
b A LaTex expression showing n + 1
c A LaTex expression showing (n + 1)(n - 1)
d A LaTex expression showing (n + 1) to the power of 2