Question

Determine if the following expressions are equivalent by first finding the value of each expression (show your work). State which (if any) are equivalent expressions and explain how you know. a. 2 2 ∙ 3 2 − 2 3 − 1 b. 2 2 ∙ (32 − 2 3 ) − 1 c. (2 ∙ 3)2 − 2 3 − 1 please help

Answer 1

Answer:

algebra we are doing arithmetic with just one new feature − we use letters to represent numbers. Because the letters are simply stand-ins for numbers, arithmetic is carried out exactly as it is with numbers. In particular the laws of arithmetic (commutative, associative and distributive) hold.

For example, the identities

2 + x = x + 2 2 × x = x × 2

(2 + x) + y = 2 + (x + y) (2 × x) × y = 2 × (x × y)

6(3x + 1) = 18x + 6

hold when x and y are any numbers at all.

In this module we will use the word pronumeral for the letters used in algebra. We choose to use this word in school mathematics because of confusion that can arise from the words such as ‘variable’. For example, in the formula E = mc2, the pronumerals E and m are variables whereas c is a constant.

Pronumerals are used in many different ways. For example:

Substitution: ‘Find the value of 2x + 3 if x = 4.’ In this case the pronumeral is given the value 4.

Solving an equation: ‘Find x if 2x + 3 = 8.’ Here we are seeking the value of the pronumeral that makes the sentence true.

Identity: ‘The statement of the commutative law: a + b = b + a.’ Here a and b can be any real numbers.

Formula: ‘The area of a rectangle is A = lw.‘ Here the values of the pronumerals are connected by the formula.

Equation of a line or curve: ‘The general equation of the straight line is y = mx + c.’

Here m and c are parameters. That is, for a particular straight line, m and c are fixe