b(12a - 3)-(a - b)(3 + b)
b(12a - 3) = b x 12a - 3 x b
b(12a - 3) = 12ab - 3b

(a - b)(3 + b) = a(3 + b)- b(3 + b)
(a - b)(3 + b) = a x 3 + a x b - b x 3 - b x b
(a - b)(3 + b) = 3a + ab - 3b - b²

b(12a - 3)-(a - b)(3 + b) = 12ab - 3b - (3a + ab - 3b - b²)
b(12a - 3)-(a - b)(3 + b) = 12ab - 3b - 3a - ab + 3b + b²
b(12a - 3)-(a - b)(3 + b) = 12ab - ab - 3b + 3b - 3a + b²
b(12a - 3)-(a - b)(3 + b) = 11ab + 0 - 3a + b²
b(12a - 3)-(a - b)(3 + b) = - 3a + 11ab + b²
b(12a - 3)-(a - b)(3 + b) = b² + 11ab - 3a

Product means multiplication

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

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

(2x - 3) x (2x + 3) = 4x² + 6x - 6x - 9

(2x - 3) x (2x + 3) = 4x² + 0 - 9

(2x - 3) x (2x + 3) = 4x² - 9

ALTERNATIVELY

(2x - 3) x (2x + 3) is a perfect of two squares

Perfect of two squares rules

(a - b)(a + b) = a² - b²

NOTE: when you are given an expressing like this a² - b², you could also express it as (a - b)(a + b)

(2x - 3) x (2x + 3) = (2x)² - 3²

(2x - 3) x (2x + 3) = 2² x x² - 9

(2x - 3) x (2x + 3) = 4x² - 9

(4x + 2)(x - 2) - 3x²

Expand the brackets

(4x + 2)(x - 2)

Concept

(a + b)(c - d) = a x (c - d)+ b x (c - d)

(4x + 2)(x - 2) = 4x x (x - 2) + 2 x (x - 2)

(4x + 2)(x - 2) = 4x x x - 2 x 4x + 2 x x - 2 x 2

(4x + 2)(x - 2) = 4x² - 8x + 2x - 4

(4x + 2)(x - 2) = 4x² - 6x - 4

(4x + 2)(x - 2) - 3x² = 4x² - 6x - 4 - 3x²

Group and simplify like terms

(4x + 2)(x - 2) - 3x² = 4x² - 3x² - 6x - 4

(4x + 2)(x - 2) - 3x² = x² - 6x - 4

C = 25 + 0.6x

C = cost

x = number of pages

You can change the decimals to fraction to make it easier for you to simplify

To change the decimal to fraction, write it in the form of whole number x 10^{- No. of times to move the decimal points to the right to get whole number}

For 0.6, we have to move the decimal point to the right once, to get the whole number 6

Hence 0.6 = 6 x 10^-1

The Negative Power Law

States that if the power is negative its the same as 1 over the positive power of the base

Every number to the power 1 is the same number

Hence 10¹ = 10

C = 25 + 0.6x