Card 1 of 20
EasyStudy card 1
Prompt
Factor \(a^2-b^2\).
Answer
\((a+b)(a-b)\).
MathChapter 11: Quadratic Functions
Flashcards
Factoring Differences of Squares and Perfect Square Trinomials Flashcards
Twenty cards on special identities, recognition, GCF-first factoring, and zero products.
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Session progress0 of 20 studied
Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
Factor \(a^2+2ab+b^2\).
Answer
\((a+b)^2\).
Card 3 of 20
EasyStudy card 3
Prompt
Factor \(a^2-2ab+b^2\).
Answer
\((a-b)^2\).
Card 4 of 20
EasyStudy card 4
Prompt
What three checks identify a difference of squares?
Answer
Exactly two terms, subtraction, and both terms are perfect squares.
Card 5 of 20
EasyStudy card 5
Prompt
Can \(a^2+b^2\) use the real difference-of-squares pattern?
Answer
No; it is a sum, not a difference.
Card 6 of 20
EasyStudy card 6
Prompt
What middle term confirms a positive perfect-square trinomial?
Answer
\(+2ab\).
Card 7 of 20
EasyStudy card 7
Prompt
What middle term confirms a negative perfect-square trinomial?
Answer
\(-2ab\).
Card 8 of 20
MediumStudy card 8
Prompt
What should you do before applying a special pattern?
Answer
Factor out the greatest common factor.
Card 9 of 20
MediumStudy card 9
Prompt
State the Zero Product Property.
Answer
If \(uv=0\), then \(u=0\) or \(v=0\).
Card 10 of 20
MediumStudy card 10
Prompt
When can the Zero Product Property be used?
Answer
Only when a product is equal to zero.
Card 11 of 20
MediumStudy card 11
Prompt
Why is \(a^2-b^2\ne(a-b)^2\)?
Answer
The square expands to \(a^2-2ab+b^2\), which has a middle term.
Card 12 of 20
MediumStudy card 12
Prompt
Factor \(9x^2-25\).
Answer
\((3x+5)(3x-5)\).
Card 13 of 20
MediumStudy card 13
Prompt
Factor \(x^2+12x+36\).
Answer
\((x+6)^2\).
Card 14 of 20
MediumStudy card 14
Prompt
Factor \(4x^2-20x+25\).
Answer
\((2x-5)^2\).
Card 15 of 20
MediumStudy card 15
Prompt
Solve \((x-3)(x+8)=0\).
Answer
\(x=3\) or \(x=-8\).
Card 16 of 20
MediumStudy card 16
Prompt
What identity evaluates \(u^2-v^2\) from a known sum and difference?
Answer
\(u^2-v^2=(u+v)(u-v)\).
Card 17 of 20
HardStudy card 17
Prompt
Factor \(12x^3-75x\) completely.
Answer
\(3x(2x+5)(2x-5)\).
Card 18 of 20
HardStudy card 18
Prompt
How do you verify a perfect-square factorization?
Answer
Expand the square and confirm both outer squares and the exact middle term.
Card 19 of 20
HardStudy card 19
Prompt
Why must both zero-product roots be kept?
Answer
Either factor can be zero, so each factor creates a possible solution.
Card 20 of 20
HardStudy card 20
Prompt
What is the recognition trap in \(x^2+8x+9\)?
Answer
The outer terms are squares, but \(8x\) is not \(2(x)(3)=6x\).
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