This math topic focuses on simplifying algebraic expressions involving the difference of squares. Students are presented with problems where they simplify expressions framed as a fraction, with a difference of squares in the numerator and a linear binomial in the denominator. Specific skills practiced include recognizing and applying the difference of squares formula, \((a^2 - b^2 = (a+b)(a-b))\), to simplify algebraic fractions by canceling common factors between the numerator and the denominator. These problems are part of an advanced unit on polynomials and quadratics.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Polynomial Algebra Difference of Squares - Variables and Integers Divided by Term - Simplify Worksheet

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Polynomial Algebra Difference of Squares - Variables and Integers Divided by Term - Simplify
1
A LaTex expression showing \frac{c to the power of 2 - 1}{c + 1}
What does this expression simplify to?
a A LaTex expression showing (c - 1)
b A LaTex expression showing (c + 1)
2
A LaTex expression showing \frac{b to the power of 2 - 16}{b - 4}
What does this expression simplify to?
a A LaTex expression showing (b + 4)
b A LaTex expression showing (b - 4)
3
A LaTex expression showing \frac{c to the power of 2 - 81}{c - 9}
What does this expression simplify to?
a A LaTex expression showing (c + 9)
b A LaTex expression showing (c - 9)
4
A LaTex expression showing \frac{x to the power of 2 - 9}{x + 3}
What does this expression simplify to?
a A LaTex expression showing (x + 3)
b A LaTex expression showing (x - 3)
5
A LaTex expression showing \frac{d to the power of 2 - 16}{d + 4}
What does this expression simplify to?
a A LaTex expression showing (d - 4)
b A LaTex expression showing (d + 4)
6
A LaTex expression showing \frac{p to the power of 2 - 25}{p + 5}
What does this expression simplify to?
a A LaTex expression showing (p - 5)
b A LaTex expression showing (p + 5)
7
A LaTex expression showing \frac{x to the power of 2 - 49}{x - 7}
What does this expression simplify to?
a A LaTex expression showing (x - 7)
b A LaTex expression showing (x + 7)
8
A LaTex expression showing \frac{p to the power of 2 - 25}{p - 5}
What does this expression simplify to?
a A LaTex expression showing (p - 5)
b A LaTex expression showing (p + 5)