which expressions are equivalent to 2(4f+2g)
select all that apply
8f+4g
2f+(4+2g)
8f+2g
4(2f+g)
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)
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)