Difference of Squares

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Show your work for each problem.

1.
Which expression is a difference of squares?
1. a) $x^2 - 25$
2. b) $x^2 - 5$
3. c) $x - 25$
4. d) $x^2 + 25$
2.
Fill in the boxes to factor $x^2 - 9$ : $x^2 - 9 = (x + \square)(x - \square)$ . What number goes in both boxes?
3.
Factor $x^2 - 49$ step by step.
4.
What is the factored form of $y^2 - 100$ ?
1. a) $(y - 10)(y - 10)$
2. b) $(y + 100)(y - 100)$
3. c) $(y + 10)(y - 10)$
4. d) $(y + 50)(y - 50)$
5.
Factor $a^2 - 36$ step by step.
6.
Fill in the boxes to factor $4x^2 - 25$ : $4x^2 - 25 = (\square + 5)(\square - 5)$ . What goes in both boxes?
7.
Which of the following can NOT be factored as a difference of squares?
1. a) $9y^2 - 1$
2. b) $x^2 - 16$
3. c) $x^2 + 16$
4. d) $25 - z^2$
8.
Factor $16m^2 - 81$ step by step.
9.
Fill in the boxes to factor $49 - y^2$ : $49 - y^2 = (\square + y)(\square - y)$ . What number goes in both boxes?
10.
Factor $25a^2 - 4b^2$ step by step.
11.
Use mental math: What is $47 \times 53$ ?
1. a)2500
2. b)2401
3. c)2509
4. d)2491
12.
Factor $x^4 - 16$ completely. The result has three factors: $(x^2 + 4)(x + \square)(x - \square)$ . What number goes in both boxes?
13.
Factor completely: $81 - x^4$
14.
Factor $16x^4 - 1$ completely. How many factors does the result have?
1. a)Cannot be factored
2. b)3 factors
3. c)4 factors
4. d)2 factors
15.
Use mental math: Calculate $98 \times 102$
16.
Factor: $36x^4 - 49y^2$
17.
Fill in the boxes to factor $x^2 - 1$ : $x^2 - 1 = (x + \square)(x - \square)$ . What number goes in both boxes?
18.
A square garden has side length $(x + 5)$ meters. In the middle is a square pond with side length $(x - 5)$ meters. Find the area of the garden around the pond.