# EXPANDING SPECIAL PRODUCTS

Expand the following :

Problem 1 :

(x - 2)2

Solution :

Use the rule for (a - b)2.

(a - b)2 = a2 - 2ab + b2

Identify a and b : a = x and b = 2.

(x - 2)2 = x2 - 2(x)(2) + 22

= x2 - 4x + 4

Problem 2 :

(a + 3)2

Solution :

Use the rule for (a + b)2.

(a + b)2 = a2 + 2ab + b2

Identify a and b : a = a and b = 3.

(a + 3)2 = a2 + 2(a)(3) + 32

= a2 + 6a + 9

Problem 3 :

(x - 5)2

Solution :

Use the rule for (a - b)2.

(a - b)2 = a2 - 2ab + b2

Identify a and b : a = x and b = 5.

(x - 5)2 = x2 - 2(x)(5) + 52

= x2 - 10x + 25

Problem 4 :

(x + 4)2

Solution :

Use the rule for (a + b)2.

(a + b)2 = a2 + 2ab + b2

Identify a and b : a = x and b = 4.

(x + 4)2 = x2 + 2(x)(4) + 42

= x2 + 8x + 16

Problem 5 :

(a - 1/2)2

Solution :

Use the rule for (a - b)2.

(a - b)2 = a2 - 2ab + b2

Identify a and b : a = a and b = 1/2.

(a - 1/2)2 = a2 - 2(a)(1/2) + (1/2)2

= a2 - a + 1/4

Problem 6 :

(x + 10)2

Solution :

Use the rule for (a + b)2.

(a + b)2 = a2 + 2ab + b2

Identify a and b : a = x and b = 10.

(x + 10)2 = x2 + 2(x)(10) + (10)2

= x2 + 20x + 100

Problem 7 :

(x - 10)2

Solution :

Use the rule for (a - b)2.

(a - b)2 = a2 - 2ab + b2

Identify a and b : a = x and b = 10.

(x - 10)2 = x2 - 2(x)(10) + (10)2

= x2 - 20x + 100

Problem 8 :

(a + 0.8)2

Solution :

Use the rule for (a + b)2.

(a + b)2 = a2 + 2ab + b2

Identify a and b : a = a and b = 0.8.

(a + 0.8)2 = a2 + 2(a)(0.8) + (0.8)2

= a2 + 1.6a + 0.64

Problem 9 :

(2x - 1)2

Solution :

Use the rule for (a - b)2.

(a - b)2 = a2 - 2ab + b2

Identify a and b : a = 2x and b = 1.

(2x - 1)2 = (2x)2 - 2(2x)(1) + 12

= 4x2 - 4x + 1

Problem 10 :

(3x + 2)2

Solution :

Use the rule for (a + b)2.

(a + b)2 = a2 + 2ab + b2

Identify a and b : a = 3x and b = 2.

(3x + 2)2 = (3x)2 + 2(3x)(2) + 22

= 9x2 + 12x + 4

Problem 11 :

(3a + 5b)2

Solution :

Use the rule for (a + b)2.

(a + b)2 = a2 + 2ab + b2

Identify a and b : a = 3a and b = 5b.

(3a + 5b)2 = (3a)2 + 2(3a)(5b) + (5b)2

= 9a2 + 30ab + 25b2

Problem 12 :

(5a - 3b)2

Solution :

Use the rule for (a - b)2.

(a - b)2 = a2 - 2ab + b2

Identify a and b : a = 5a and b = 3b.

(5a - 3b)2 = (5a)2 - 2(5a)(3b) + (3b)2

= 25a2 - 30ab + 9b2

Problem 13 :

(x - 3) (x + 3)

Solution :

Use the rule for (a - b) (a + b).

(a - b) (a + b) = a2 - b2

Identify a and b : a = x and b = 3.

(x - 3) (x + 3) = x2 - 32

(x - 3) (x + 3) = x2 - 9

Problem 14 :

(x + 4) (x - 4)

Solution :

Use the rule for (a + b) (a - b).

(a + b) (a - b) = a2 - b2

Identify a and b : a = x and b = 4.

(x + 4) (x - 4) = x2 - 42

(x + 4) (x - 4) = x2 - 16

Problem 15 :

(a + 5) (a - 5)

Solution :

Use the rule for (a + b) (a - b).

(a + b) (a - b) = a2 - b2

Identify a and b : a = a and b = 5.

(a + 5) (a - 5) = a2 - 52

(a + 5) (a - 5) = a2 - 25

Problem 16 :

(a - 6) (a + 6)

Solution :

Use the rule for (a - b) (a + b).

(a - b) (a + b) = a2 - b2

Identify a and b : a = a and b = 6.

(a - 6) (a + 6) = a2 - 62

(a - 6) (a + 6) = a2 - 36

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