Question

Which of the following statements are true for all real numbers, and z? Choose all that apply:

A) x+y+z=y+(x+z)
B) x(y-z)=xy-xz
C) xy+z=x(y+z)
D) None of the above

Answer 1

Statements A) x+y+z=y+(x+z) and B) x(y-z)=xy-xz are true for all real numbers, based on the associative property of addition and the distributive law of multiplication respectively. Statement C) xy+z=x(y+z) is not true.

Step-by-step explanation:

Out of the given statements regarding real numbers and arithmetic operations, let's identify which ones are true for all real numbers x, y, and z:

• A) x+y+z=y+(x+z) is true. It reflects the associative property of addition, meaning that when you add three numbers, the way in which you group them does not affect the sum. Addition is associative, which means that (x+y)+z = x+(y+z).
• B) x(y-z)=xy-xz is true. This is the distribution law of multiplication over subtraction. Essentially, you are multiplying x with both y and -z and then combining the terms.
• C) xy+z = x(y+z) is not true. This equation confuses the distributive property and is an incorrect application of it. Correctly applied, the distributive property states that x(y+z) = xy + xz.
• D) None of the above is false since statements A and B are true.

Therefore, the correct choices are A) x+y+z=y+(x+z) and B) x(y-z)=xy-xz.