Card 1 of 8
MediumStudy card 1
Prompt
How does a difference of squares factor?
Answer
a² − b² = (a − b)(a + b).
Difference of squares
\[a^2-b^2=(a-b)(a+b)\]
MathAdvanced Math
Flashcards
Equivalent Expressions Flashcards
Recall factoring patterns, exponent laws, and safe simplification.
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Card 1 of 8. Answer hidden.
Card 2 of 8
MediumStudy card 2
Prompt
What is the perfect-square trinomial pattern?
Answer
a² ± 2ab + b² = (a ± b)².
Perfect-square identity
\[a^2\pm2ab+b^2=(a\pm b)^2\]
Card 3 of 8
MediumStudy card 3
Prompt
What should you check before using a special factoring pattern?
Answer
A greatest common factor shared by every term.
Card 4 of 8
MediumStudy card 4
Prompt
How do exponents combine when multiplying like bases?
Answer
Add the exponents.
Product of powers
\[x^m x^n=x^{m+n}\]
Card 5 of 8
MediumStudy card 5
Prompt
How do exponents combine when raising a power to a power?
Answer
Multiply the exponents.
Power of a power
\[(x^m)^n=x^{mn}\]
Card 6 of 8
MediumStudy card 6
Prompt
What may be canceled in a rational expression?
Answer
Common factors of the entire numerator and denominator—not individual terms joined by addition.
Card 7 of 8
HardStudy card 7
Prompt
Can simplifying remove an original domain restriction?
Answer
No. Values that made the original denominator zero remain excluded.
Card 8 of 8
MediumStudy card 8
Prompt
Which equivalent form is best?
Answer
The form that exposes the requested feature: factors for zeros, expanded form for coefficients, or vertex form for extrema.
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