Question

Are the expressions equivalent?

1) 3t +5 and 3(5)+ t
2) bxy+by and ybx+ xb
3) 4x and x+4
4) ab + bc and b(a+c)
5) a+c+e+g and ea+cq

Answer 1

The student queried about the equivalency of various mathematical expressions. Only some of them are equivalent due to commutative and distributive properties whereas others are not equivalent due to differences in operations and terms.

Step-by-step explanation:

The student is asking whether certain mathematical expressions are equivalent. Let's analyze each pair:

• 1) 3t + 5 and 3(5) + t: These expressions are not equivalent because 3(5) gives us 15. Thus, the second expression simplifies to 15 + t, which is not the same as 3t + 5.
• 2) bxy + by and ybx + xb: These expressions are equivalent because multiplication is commutative (the order does not matter). Both simplify to by(x + 1).
• 3) 4x and x + 4: These expressions are not equivalent. The first expression is 4 times x, while the second is the sum of x and 4.
• 4) ab + bc and b(a + c): These expressions are equivalent by the distributive property. b(a + c) distributes to become ab + bc.
• 5) a + c + e + g and ea + cq: These expressions are not equivalent. The first is a sum of four terms, while the second is two terms that suggest multiplication and are missing two variables from the first expression.

It's important to remember that in order for expressions to be equivalent, they must yield the same result for any substitution of the variables involved.