Question

for each expression, select all equivalent expressions from the list. (a) 7x + 21 (b) 14+13y - 6 - y 7·x+7·3 7(x + 3) 28x 7(3x + 1) 12 + 8y 8y+12 8y + 12 12y+8

Explanation:

Step1: Simplify expression (a)

For the expression \(7x + 21\), we can use the distributive - property. We know that \(7x+21 = 7\cdot x+7\cdot3\) and also \(7x + 21=7(x + 3)\) by factoring out the common factor 7.

Step2: Simplify expression (b)

For the expression \(14 + 13y-6 - y\), combine like - terms. Combine the constant terms \(14-6 = 8\) and the y - terms \(13y-y=12y\). So \(14 + 13y-6 - y=8y + 8\).

Answer:

(a) \(7\cdot x+7\cdot3\), \(7(x + 3)\)
(b) None of the given options are equivalent.