Apply the properties of operations to determine which expression is equivalent to a+b+c(d+2) .(1 point) Responses 2abcd 2 a b c d a+b+cd+2c a plus b minus c d minus 2 c a+b+cd+2 a plus b minus c d plus 2. 2.Are the expressions 3−(4x+1) and 4−4x equivalent? A. Yes, they are because both expressions simplify to 4−4x. B. Yes, they are because both expressions simplify to 0. C. No, they are not because 3−(4x+1) simplifies to 2−4x , which is not equivalent to 4−4x. D. No, they are not because 3−(4x+1) simplifies to −1x+1, which is not equivalent to 4−4x
Based on the properties of operations,
The expression a+b+c(d+2) can be simplified as follows:
a+b+c(d+2)
= a+b+cd+2c (By using the distributive property)
Therefore, the expression equivalent to a+b+c(d+2) is a+b+cd+2c.
For the second question,
The expression 3−(4x+1) can be simplified as follows:
3−(4x+1)
= 3−4x−1 (By applying the distributive property with the negative sign)
= 2−4x
The expression 4−4x remains as it is.
Since 2−4x is not equal to 4−4x, the expressions 3−(4x+1) and 4−4x are not equivalent.
So, the answer is D. No, they are not because 3−(4x+1) simplifies to −1x+1, which is not equivalent to 4−4x.
which expression is equivalent to 5(g+2)-3
5g-1
5g+7
5g+10
5g-7
To simplify the expression 5(g+2)-3, we can use the distributive property:
5(g+2) = 5g + 10
Now we can substitute this back into the original expression:
5(g+2)-3 = 5g + 10 - 3 = 5g + 7
Therefore, the expression equivalent to 5(g+2)-3 is 5g + 7
apply the disruptive property to generate an expression equivalent to 8(3+j)
24+j
11+8j
24+8j
24-j
To apply the distributive property to the expression 8(3+j), we need to multiply each term inside the parentheses by 8:
8(3+j) = 8*3 + 8*j
This simplifies to:
24 + 8j
Therefore, the expression equivalent to 8(3+j) is 24 + 8j.