Question

Select all the expressions equivalent to 2(x + 3). Explain your reasoning. A 2 ⋅ (x + 3) B (x + 3)2 C 2 ⋅ x + 2 ⋅ 3 D 2 ⋅ x + 3 E (2 ⋅ x) + 3 F (2 + x)3

Answer 1

A and B

Explanation:

In this question, we are asked to pick the options which have the same value as the expression in the question.

Firstly, let’s expand the main expression in the question.

Mathematically, expanding this, we have 2x + 6

now let’s consider the options one after the other.

Options A and B are correct as they mean the same thing and would refer to the expression in the question.

Option c is wrong. Expanding option c would yield 2x + 4

option d is wrong as the multiplication is only between 2 and x and does not cover 3. This makes the expression as 2x + 3

option E is is also wrong as it is same as D but expressed in another fashion

option F is is wrong also as expanding would give 6 + 3x which is different from 2x + 6

Answer 2

Answer: B and A

Explanation:

(X+3)2 = 2×x + 2×3

= 2x + 6

Likewise

2(x+3) = 2×x +. 2×3

= 2x + 6

Hence they are both same

2.(X +3) still equivalent to 2x +6