Question

Which expressions are equivalent to 2(4f+2g)

Answer 1

Answer:

Option (a) and (d) are correct .

An equivalent expression to the given expression  2(4f + 2g) is  8f + 4g

and 4 (2f + g)

Step-by-step explanation:

Given: Expression 2(4f + 2g)

We have to choose an equivalent expression to the given expression  2(4f + 2g)

Consider the given expression 2(4f + 2g)  

Apply Distributive property, $\:a\left(b+c\right)=ab+ac$

We have,

a = 2, b = 4f and c = 2g

2(4f + 2g) = 8f + 4g

Now, take 4 common from each term, we have,

8f + 4f = 4 (2f + g)

Thus, an equivalent expression to the given expression  2(4f + 2g) is  8f + 4g and 4 (2f + g)

Answer 2

Answer:

Option A and D are correct

8f + 4g and $4 \cdot (2f+g)$

Step-by-step explanation:

The distributive property says that:

$a\cdot (b+c) = a\cdot b+ a\cdot c$

Given the expression:

$2 \cdot (4f+2g)$

Using distributive property;

$2 \cdot 4f+ 2 \cdot 2g = 8f+4g$

⇒$2 \cdot (4f+2g)$ = 8f+4g               ....[1]

Option A.

8f + 4g      

which is equal to the given expression in  [1]

Option B.

$2f +(4+2g) = 2f+4+2g = 2f+2g+4$

which is not equal to given expression in  [1]

Option C.

8f + 4g      

which is not equal to the given expression in [1]

Option D.

$4 \cdot (2f+g)$

Using distributive property we have;

$8f+4g$

which is equal to the given expression in  [1]

Therefore, 8f + 4g and $4 \cdot (2f+g)$ expressions are equivalent to 2(4f+2g)