Question

Determine whether the two expressions are equivalent. Explain your reasoning.

Answer 1

Let us evaluate each pair of expressions one at a time.
8. (n²+4) - n² and 4n.
    (n²+4) - n² = n²+ 4 - n² = 4 which is not equal to 4n.
    NOT EQUIVALENT

9. 3x + 5 and  2(x + 3)
    2(x + 3) = 2x + 6  which is not equal to 3x + 5.
    NOT EQUIVALENT

10. 15 - 6x and  15(1 - 6x)
    15(1 - 6x) = 15 - 90x which is not equal to 15 - 6x
    NOT EQUVALENT

11. (y + y + 2 + y) + 3y and 6y + 2
    (y +y +2 + y) + 3y = y+y+y +2 + 3y = 3y + 2 + 3y = 6y + 2.
    It matches the other expression.
    EQUIVALENT

12. 8y - 3 + 10y and 3(6 - 1)
    8y - 3 + 10y = 8y + 10y - 3 = 18y - 3
    3(6 - 1) = 3(5) = 15
    The two expressions do not match.
    NOT EQUIVALENT.

Answer: Only the expressions in number 11 are equivalent.