Mathematics

Factorisation

100

a¹²x⁴  -  a⁴x¹²

a⁴x⁴ (a⁴ + x⁴)(a² + x²)(a+x)(a-x)

100

4a² + 12ab + 9b² - 8a - 12b

(2a + 3b)(2a +3b - 4)

100

x¹² - y¹²

(x² + y²)(x-y)(x+y)(x² + xy + y²)(x² - xy + y²)(x⁴ + x²y² + y⁴)

100

x⁴ + 4x² + 3

(x² + 3)(x² + 1)

100

x² - y² - 4xz + 4z²

(x + y - 2z)(x - y - 2z)

Factorisation

100

a³ - 1/a³ -2a + 2/a

(a - 1/a)(a² +1/a² - 1)

100

7.2^1/2.x² - 10x -4.2^1/2

(x - 2^1/2)(7.2^1/2.x + 4)

100

x⁴ + 5x² + 9

(x² - x + 3)(x² + x + 3)

100

x³ - 3x² + 3x + 7

(x+1)(x² - 4x + 7)

100

1 - 2ab - (a² + b²)

(1 + a + b)(1 - a - b)

Expansion

100

(-12)³ + 7³ + 5³

-1260

100

If, x² + 1/x² = 83, Find x³ - 1/x³

756

100

If a - b = 4  &  ab=45, find a³ - b³

604

100

If x + 1/x = 5^1/2

Find x⁴ + 1/x⁴

7

100

If,  9x² + 25y² = 181  &  xy = -6

Find 3x + 5y

+- 1

Exponents

100

Simplify :

(16. 2ⁿ⁺¹ - 4.2ⁿ) / (16.2ⁿ⁺² - 2.2ⁿ⁺²)

1/2

100

If 5^x-3. 3^2x-8 = 225

Find x

5

100

Simplify (11^1/2 + 3^1/2)^1/3 (11^1/2 - 3^1/2)^1/3

2

100

Solve : (25)^x-1 = 5^y+1 ; 

(1/3)^3-x = (1/9)^2y

x = 5/3 ; y = 1/3

100

[ {(64)^5n/6 . (27)^-n/6} / (12)^-n/2 ] .2⁶ⁿ

2¹²ⁿ