Special Products

Show your work for each problem.

1.
Which formula represents the square of a sum ?
1. a)
2. b)
3. c)
4. d)
Answer:
. The middle term comes from multiplying and twice: once as and once as .
2.
Expand . What is the coefficient of the middle term?
Answer: 6
. The middle term is , so the coefficient is .
3.
What is ?
1. a)
2. b)
3. c)
4. d)
Answer:
. The middle terms cancel out when multiplying conjugates.
4.
Expand
Answer: x^2 + 4x + 4
1. What is (first term squared)? x^2
2. What is (the middle term)? 4x
3. What is (last term squared)? 4
5.
What is the constant term in the expansion of ?
Answer: 16
. The constant term is .
6.
What is ?
1. a)
2. b)
3. c)
4. d)
Answer:
7.
Expand
Answer: 9x^2 - 12x + 4
1. What is ? 9x^2
2. What is ? -12x
3. What is ? 4
8.
What is ? Give the constant term only.
Answer: -4
. The constant term is .
9.
Which expression equals ?
1. a)
2. b)
3. c)
4. d)
Answer:
. The middle term is negative, but the constant is positive.
10.
Expand
Answer: 16x^2 - 1
1. What pattern is this? difference of squares
2. What is ? 16x^2
3. What is ? 1
11.
Calculate using the difference of squares pattern.
Answer: 399
12.
Expand
Answer: 4x^2 + 20x + 25
1. What is ? 4x^2
2. What is ? 20x
3. What is ? 25
4. Combine: What is the full expansion? 4x^2 + 20x + 25
13.
What is ?
1. a)
2. b)
3. c)
4. d)
Answer:
. The middle terms cancel.
14.
Calculate using special products.
Answer: 896
15.
Expand
Answer: 25x^2 - 30x + 9
1. What is ? 25x^2
2. What is ? -30x
3. What is ? 9
4. What is the full expansion? 25x^2 - 30x + 9
16.
What is the coefficient of in the expansion of ?
Answer: 36
. The coefficient of is .
17.
Calculate using the square of a sum.
Answer: 2601
1. Write 51 as 1
2. What is ? 2500
3. What is ? 100
4. What is ? 1
5. Add them all: 2601