Practice Algebraic Pattern in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A recognizable, recurring algebraic structure such as or that can be applied systematically.
always factors to — recognize the pattern once and apply it everywhere.
Showing a random 20 of 50 problems.
Example 1
hardSimplify for .
Example 2
mediumA trinomial is a perfect square. Find all values of .
Example 3
easyFactor by finding the additive/multiplicative pattern.
Example 4
mediumThe sequence follows what pattern? Give a formula for .
Example 5
mediumFactor using the sum-of-cubes pattern.
Example 6
challengeRecognize the pattern in and prove the closed form using the binomial theorem.
Example 7
mediumUse a pattern to compute .
Example 8
easyRecognize the pattern: . What is the -th term?
Example 9
hardRecognize and factor: .
Example 10
easyIs factorable over the reals as a difference of squares?
Example 11
mediumFactor by recognizing the disguised pattern.
Example 12
mediumFactor .
Example 13
challengeFor which integer is factorable over the integers as a product of two quadratics? Use the Sophie Germain pattern.
Example 14
mediumUse a pattern to compute without long multiplication.
Example 15
easyIs a difference of squares?
Example 16
mediumThe pattern telescopes. Recognize the term pattern and sum it.
Example 17
challengeFind a closed form for the telescoping sum .
Example 18
easyIdentify the pattern and factor: .
Example 19
mediumFind so that is a perfect square.
Example 20
easyFactor by recognizing the pattern.