Question

How do you use distributive property to rewrite and simplify $2\left( x+4 \right)$ ?

Answer 1

Hint: To simplify $2\left( x+4 \right)$ , we will be using distributive property. We have to consider $a\left( b+c \right)$ . We can solve this by multiplying each term inside the bracket by a. This means that, a is ‘distributed’ to b and c. Thus, we can write $a\left( b+c \right)=ab+ac$ . In this way, we can solve the given question.

Complete step by step solution:
We have to use distributive property to simplify $2\left( x+4 \right)$ . Let us see what distributive property is. Let us consider $a\left( b+c \right)$ . We can solve this by multiplying each term inside the bracket by a. We can say that, a is ‘distributed’ to b and c. Thus, we can write
$a\left( b+c \right)=ab+ac$ .
Now, let us solve $2\left( x+4 \right)$ . We have to multiply each term inside the bracket by 2. We will get
$2\left( x+4 \right)=\left( 2\times x \right)+\left( 2\times 4 \right)$
Let us simplify this. When we multiply the terms, we will get
$\Rightarrow 2\left( x+4 \right)=2x+8$
Hence, the answer is $2x+8$ .

Note: Students must know basic number properties like associative, commutative and distributive properties. Associative property states that when different numbers are added or multiplied, they can be grouped in different ways without changing their sum or product. We can see that $7\times \left( 2\times 3 \right)=\left( 7\times 2 \right)\times 3$ . Also $3+\left( 2+5 \right)=\left( 3+2 \right)+5$ . In general, we can say that $a.\left( b.c \right)=\left( a.b \right).c\text{ or }a+\left( b+c \right)=\left( a+b \right)+c$ . Commutative property states that when two numbers are added or multiplied, their order can be changed without any change in their sum or product. We can write it in general as $a+b=b+a$ and $a.b=b.a$ .