Card 1 of 20
EasyStudy card 1
Prompt
What does FOIL organize?
Answer
The four distributive products for two binomials: first, outer, inner, and last.
MathChapter 10: Law of Exponents and Polynomials
Flashcards
FOIL Method and Special Products Flashcards
Recall complete distribution, special-product identities, recognition clues, and common errors.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
What should happen after the four FOIL products are written?
Answer
Combine the two like middle terms.
Card 3 of 20
EasyStudy card 3
Prompt
Expand \((a+b)^2\).
Answer
\(a^2+2ab+b^2\)
Formula
\[(a+b)^2=a^2+2ab+b^2\]
Card 4 of 20
EasyStudy card 4
Prompt
Expand \((a-b)^2\).
Answer
\(a^2-2ab+b^2\)
Formula
\[(a-b)^2=a^2-2ab+b^2\]
Card 5 of 20
EasyStudy card 5
Prompt
Expand \((a+b)(a-b)\).
Answer
\(a^2-b^2\)
Formula
\[(a+b)(a-b)=a^2-b^2\]
Card 6 of 20
MediumStudy card 6
Prompt
Why does a conjugate product have no middle term?
Answer
Its outer and inner products are opposites and cancel.
Card 7 of 20
EasyStudy card 7
Prompt
What is the most common error in squaring a binomial?
Answer
Omitting the middle term \(\pm2ab\).
Card 8 of 20
EasyStudy card 8
Prompt
What sign does the final term of \((a-b)^2\) have?
Answer
Positive, because \((-b)(-b)=b^2\).
Card 9 of 20
EasyStudy card 9
Prompt
Expand \((x+5)^2\).
Answer
\(x^2+10x+25\)
Card 10 of 20
MediumStudy card 10
Prompt
Expand \((3x-4)^2\).
Answer
\(9x^2-24x+16\)
Card 11 of 20
MediumStudy card 11
Prompt
Expand \((2y+7)(2y-7)\).
Answer
\(4y^2-49\)
Card 12 of 20
MediumStudy card 12
Prompt
How can you recognize a perfect-square trinomial?
Answer
The ends are squares and the middle term is twice the signed product of their square roots.
Card 13 of 20
MediumStudy card 13
Prompt
Is \(x^2+16\) a conjugate product over real polynomials?
Answer
No. Conjugates produce a difference of squares, not a sum of squares.
Card 14 of 20
MediumStudy card 14
Prompt
Which method works when one factor has three terms?
Answer
Use the full Distributive Property; FOIL's four labels apply only to two binomials.
Card 15 of 20
MediumStudy card 15
Prompt
For \((x+m)(x+n)\), what is the middle coefficient?
Answer
\(m+n\)
Formula
\[(x+m)(x+n)=x^2+(m+n)x+mn\]
Card 16 of 20
MediumStudy card 16
Prompt
For \((x+m)(x+n)\), what is the constant term?
Answer
\(mn\)
Card 17 of 20
MediumStudy card 17
Prompt
What structural predictions can you make before expanding a binomial square?
Answer
It will have three terms; the last is positive; the middle sign matches the binomial sign.
Card 18 of 20
HardStudy card 18
Prompt
How do you prove that an expanded expression matches a binomial product?
Answer
Expand symbolically and compare every coefficient by degree.
Card 19 of 20
HardStudy card 19
Prompt
What is reverse recognition?
Answer
Using an expanded polynomial's end terms and middle term to identify the special product that generated it.
Card 20 of 20
HardStudy card 20
Prompt
Why is matching only the first and last terms unsafe?
Answer
Different products can share the same ends; the middle coefficient and sign distinguish the identity.
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