Question

An equivalent expression to 43(−2+10) is 43(−2)

Answer 1

The expression 43(−2+10) is not equivalent to 43(−2). By utilizing the distributive property and performing the operations, we find that 43(−2+10) equals 344, whereas 43(−2) equals −86.

Step-by-step explanation:

The student has asked whether the expression 43(−2+10) is equivalent to 43(−2). To determine the equivalency of these expressions, we need to use the distributive property of multiplication over addition.

1. Apply the distributive property: 43(−2 + 10) = 43(×−2) + 43(×10).
2. Perform the multiplications: −86 + 430.
3. Add the results: −86 + 430 = 344.

Now, let's look at the expression 43(−2):

1. Multiply 43 by −2: 43(×−2) = −86.

The two expressions are not equivalent because 43(−2 + 10) equals 344 and 43(−2) equals −86.

Moreover, when we subtract or add numbers, there are rules for the signs described in other provided examples, but they are not directly applicable to the given expressions since they involve a combination of multiplication and addition, not only subtraction or addition.