FACTORING POLYNOMIALS USING ALGEBRAIC IDENTITIES WORKSHEET

Factorize each polynomial using algebraic identity.

Problem 1 :

36k² - 1

Solution

Problem 2 :

x² - 9y²

Solution

Problem 3 :

25m² - n²

Solution

Problem 4 :

8r³ - 729

Solution

Problem 5 :

p³ - 1000q³

Solution

Problem 6 :

27c³ + 125d³

Solution

Problem 7 :

64y³- 216

Solution

Problem 8 :

36y² + 84y + 49

Solution

Problem 9 :

h² + 4h + 4

Solution

Problem 10 :

z² - 8z + 16

Solution

Problem 11 :

25a² - 9b²

Solution

Problem 12 :

a² - 81(b - c)²

Solution

Problem 13 :

50a³ - 2a

Solution

Problem 14 :

3a⁵ - 108a³

Solution

Problem 15 :

a⁴ - 1

Solution

Problem 16 :

(a + b)³ - a - b

Solution

Problem 17 :

4a² - (4b² + 4 bc + c²)

Solution

Problem 18 :

a² - b² - (a + b)²

Solution

Problem 18 :

a³ + 27b³

Solution

Factorize each polynomial using algebraic identity.

Problem 1 :

49p² - q²

Solution

Problem 2 :

64 - d²

Solution

Problem 3 :

u² - 16v

Solution

Problem 4 :

27u³ + 343v³

Solution

Problem 5 :

c³ + 216

Solution

Problem 6 :

512z³ - 1

Solution

Problem 7 :

16p² + 56p + 49

Solution

Problem 8 :

s² + 16st + 64t²

Solution

Problem 9 :

k² - 18k + 81

Solution

Problem 10 :

m² - 6mn + 9n²

Solution

Problem 11 :

2a⁷ - 128a

Solution

Problem 12 :

a³ - 27

Solution

Problem 13 :

12(3x - 2y)² - 3x + 2y - 1

Solution

Problem 14 :

4(2x - 3y)² - 8x + 12y - 3

Solution

Problem 15 :

3 - 5x + 5y - 12(x - y)²

Solution

Factorize each polynomial using algebraic identity.

Problem 1 :

w² - 4

Solution

Problem 2 :

a² - b²

Solution

Problem 3 :

9 - 16t²

Solution

Problem 4 :

8a³ - 27b³

Solution

Problem 5 :

m³ + n³

Solution

Problem 6 :

125x³ - 64

Solution

Problem 7 :

x² + 10x + 25

Solution

Problem 8 :

36u² - 12uv + v²

Solution

Problem 9 :

4a² - 4a + 1

Solution

Problem 10 :

25x² - 36

Solution

Problem 11 :

If t > 0 and t² − 4 = 0, what is the value of t ?

Solution

Problem 12 :

If x^a²/ x^b² = 16, x > 1 and a + b = 2, what is the value of a - b ?

Solution

Problem 13 :

x² + y² + 4x - 2y = -1

The equation of a circle in the xy-plane is shown above. What is the radius of the circle ?

a)  2      b)  3     c)  4      d)  9

Solution

Problem 14 :

The equation

x² + (y - 1)² = 49

represent circle A. Circle B is obtained by shifting circle A down 2 units in the xy-plane. Which of the following equation represents circle B ?

a)  (x - 2)² + (y - 1)² = 49           b) x² + (y - 3)² = 49

c) (x + 2)² + (y - 1)² = 49           d)  x² + (y + 1)² = 49

Solution

Problem 15 :

(d − 30)(d + 30) − 7 = −7

What is a solution to the given equation?

Solution