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