➕ Algebra 1 · Factoring
Difference of Squares flashcards
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All 16 flashcards at a glance
Card 1
State the difference of squares pattern.
a2 − b2 = (a + b)(a − b). It applies to two perfect squares with a minus sign between them.
Card 2
Factor y2 − 100.
(y + 10)(y − 10)
Card 3
Factor 25n2 − 36.
(5n + 6)(5n − 6)
Card 4
Factor 3x2 − 75 completely.
3(x + 5)(x − 5). Take out the GCF 3 first: 3(x2 − 25).
Card 5
Factor 9a2 − 16b2.
(3a + 4b)(3a − 4b)
Card 6
Factor k4 − 81 completely.
(k2 + 9)(k + 3)(k − 3). First (k2 + 9)(k2 − 9), then k2 − 9 factors again.
Card 7
Can x2 + 25 be factored using integers?
No. It is a sum of squares, so it is prime (cannot be factored using integers).
Card 8
Why is x2 − 36 not equal to (x − 6)2?
(x − 6)2 = x2 − 12x + 36 has a middle term and a plus 36. The factors of a difference of squares have opposite signs, so the middle terms cancel: (x + 6)(x − 6) = x2 − 36.
Card 9
Use the pattern to find 63 × 57 in your head.
(60 + 3)(60 − 3) = 3600 − 9 = 3591
Card 10
Is x2 − 7 a difference of squares (using integers)?
No. 7 is not a perfect square, so x2 − 7 cannot be factored using integers. (If square roots are allowed it is (x + √7)(x − √7).)
Card 11
What do you square to get 49x10?
7x5. Take the square root of 49 and halve the exponent 10. Check: (7x5)2 = 49x10.
Card 12
In this lesson’s FACTS checklist for difference of squares, what do the letters stand for?
F: take out any GCF First. A: Are there two terms with one perfect square subtracted from another? C: Choose a and b. T: write Two factors, (a + b)(a − b). S: Spot-check by expanding, and Scan the factors for more factoring.
Card 13
Multiply (4k + 7)(4k − 7).
16k2 − 49. The middle terms −28k and +28k cancel.
Card 14
Factor −5x2 + 20 completely.
−5(x + 2)(x − 2). Take out −5 first: −5(x2 − 4).
Card 15
Can x2 + 9 be factored using any real numbers, not just integers?
No. At x = −p a factor (x + p) would make the product 0, but x2 + 9 is never 0 for real x. A later course uses imaginary numbers: (x + 3i)(x − 3i).
Card 16
How do you check a factoring answer?
Multiply the factors back out. You should get the original expression. For (q + 2)(q − 2) the middle terms cancel and you get q2 − 4.