Revision!!!

Expansion

100

Expand and simplify (x + 3)(x - 3)

x² - 9

200

Expand (2x + 3)².

4x² + 12x + 9

300

Expand (4x-3y)²

16x²−24xy+9y²

400

If a - b = 3 and a² + b² = 29, find the value of ab.

ab = 10

500

If 2x + 3y  =  13 and xy  =  6, then find the value of 

8x³ + 27y³

Use cubic formula (a + b)³ = a³ + b³ + 3ab(a+b)

8x³ + 27y³ = 793

Factorization

100

Factorise x² - 36

(x+6)(x-6)

200

Factorise x² + 8x + 16

(x+4)²

300

Factorize: y²+4y−21

(y+7)(y-3)

400

Factorize: 4z²−12z+9

(2z-3)²

500

The product of two consecutive positive integers is 19 more than their sum. Find the integers.

x * (x+1) = x + (x+1) + 19

=> x² + x = 2x + 20

=> x² - x - 20 = 0

x = 5

x+1 = 6

Exponents

100

Simplify: 5a²×4a³

20a⁵

200

If (2x)²=256, find the value of x.

4x² = 256

=> x² = 64

=> x = 8 or -8

300

If 3×3ⁿ=9×3⁰×27×27⁴

Find the value of n.

n = 16

400

If 2ⁿ=4^p×8ⁿ
write down an expression for n in terms of p.

2ⁿ=4^p×8ⁿ

2ⁿ=2^2p×2³ⁿ

=> n = 2p + 3n

=> 2n = -2p

=> n = -p

500

Without using a calculator, show clearly that 729^(2/3)

is equal to 3⁴.

729^(2/3) = (9³)^(2/3) = 9^3*2/3 = 9² = 81 = 3⁴