FACTORIZATION 7

Factorize a²b² - c²

Solution

We use difference of two squares M² – N² = (M -N)(M + N)

a²b² - c² = (ab)² - (c)²

              = (ab - c)( ab + c)

Hence a²b² - c² = (ab - c)( ab + c)

TRY THIS…………….

Factorize a²m² - c²

RADICALS 2

GEOMETRY 1

A regular polygon has 10 sides. Find the total angles of that polygon.

Solution

n = 10

Total angles = (n - 2)180⁰

                   = (10 – 2)180⁰

                   = 8 x 180⁰

                   = 1440⁰

∴ Total angles = 1440⁰

TRY THIS……………………….

A regular polygon has 44 sides. Find the total angles of that polygon.

LOGARITHMS 5

Evaluate Log30 – Log15 + Log50.

Solution

= Log30 – Log15 + Log50.

= Log(30 x 50)

               15

= Log(1500)

             15

= Log₁₀100

= Log₁₀10²

            

= 2Log₁₀10

= 2 x 1

= 2

∴ Log30 – Log15 + Log50 = 2

TRY THIS……………………….

Evaluate Log750 – Log15 + Log20.

FACTORIZATION 6

Factorize m²n² - c²

Solution

We use difference of two squares a² – b² = (a - b)(a + b)

m²n² - c² = (mn)² - (c)²

              = (mn - c)( mn + c)

Hence m²n² - c² = (mn - c)( mn + c)

TRY THIS…………….

Factorize e²n² - c²

RADICALS 1

BODMAS APPLICATION 1

Evaluate  71 + 6 – 5 – 7 – 9 + 4

Solution

= 71 + 6 – 5 – 7 – 9 + 4

= 71 + 6 + 4 – 5 – 7 – 9

= 71 + 6 + 4 – ( 5 + 7 + 9)

= 81 – 21

= 60

TRY THIS…………..

Evaluate  30 + 6 – 4 – 7 – 11 + 8

LOGARITHMS 4

Evaluate log₂512²⁰

Solution

= log₂512²⁰

= log₂(2⁹)²⁰

= log₂2¹⁸⁰

= 180 x log₂2    [since log_aa = 1]

= 180 x 1

= 180

Hence log₂512²⁰ = 180

TRY THIS..............

Evaluate log₂1024⁸

FACTORIZATION 5

factorize 4x²- 81y^2.

solution

we use difference of two squares a² – b² = (a - b)(a + b)

4x²- 81y² = 2²x² - 9²y²

                     = (2x)² - (3y)²

                     = (2x - 3y)( 2x + 3y)

Hence 4x² - 81y² = (2x - 3y)( 2x + 3y)

TRY THIS…………….

factorize 100a²- 625e²

FACTORIZATION 4

Factorize 625 - y^2.

solution

We use difference of two squares a² – b² = (a - b)(a + b)

625 - y² = 25²- y²

          = (25 - y)(25 + y)

Hence 16 - y² = (25 - y)(25 + y)

TRY THIS…………….

factorize 144 - w²