➕ Algebra 1 · Exponents and Polynomials
Special Products of Binomials flashcards
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All 17 flashcards at a glance
Card 1
What is the square-of-a-sum pattern?
(a + b)2 = a2 + 2ab + b2. Square the first term, double the product, square the last term.
Card 2
What is the square-of-a-difference pattern?
(a − b)2 = a2 − 2ab + b2. The middle term is −2ab, and the last term +b2 is never negative.
Card 3
What is the sum-times-difference pattern?
(a + b)(a − b) = a2 − b2. The middle terms cancel. It needs the same two terms in both factors.
Card 4
In this lesson’s S-D-S pattern, what do the letters stand for?
Square the first term, Double the product of the two terms, Square the last term. It is for a binomial squared.
Card 5
Why is (a + b)2 not a2 + b2? Test a = 2 and b = 3.
(2 + 3)2 = 25, but 22 + 32 = 13. The missing 12 is 2ab = 2 × 2 × 3, the two rectangles in the picture.
Card 6
Expand (m + 11)2.
m2 + 22m + 121
Card 7
Expand (k − 6)2.
k2 − 12k + 36
Card 8
Expand (6x + 1)2.
36x2 + 12x + 1
Card 9
Expand (−5x + 2)2.
25x2 − 20x + 4. The first term is −5x, so the double product is 2 × (−5x) × 2 = −20x.
Card 10
Expand (x + 8)(x − 8).
x2 − 64
Card 11
Use a special product to find 312 in your head.
(30 + 1)2 = 900 + 60 + 1 = 961
Card 12
Use a special product to find 29 × 31 in your head.
(30 − 1)(30 + 1) = 900 − 1 = 899
Card 13
What is the middle term of (5x − 4)2?
−40x, because 2 × 5x × (−4) = −40x. The whole answer is 25x2 − 40x + 16.
Card 14
Does a shortcut apply to (x + 3)(x − 5)? Why or why not?
No. The terms 3 and 5 are different, so the middle terms do not cancel, and it is not a square. Multiply every term by every term: x2 − 2x − 15.
Card 15
What is the cross term in (a + b)2?
The middle term 2ab, made from multiplying across the two different terms: a × b and b × a (the Outer and Inner products).
Card 16
Why can’t trying a few numbers prove an identity?
A number test checks only the values you tried, and a wrong equation can match by luck. Multiplying out with letters covers every value.
Card 17
Is (a + b)3 equal to a3 + b3?
No. Try a = 1 and b = 1: (1 + 1)3 = 8, but 13 + 13 = 2.