Final answer:
The student's question about verifying the equation 27 (34 - 58) = 27 x 34 - 27 x 58 is answered by demonstrating the distributive property of multiplication over subtraction: 27 x 34 - 27 x 58 = 918 - 1566 = -648, confirming the equality.
Step-by-step explanation:
The student's question involves verifying the equation 27 (34 - 58) = 27 x 34 - 27 x 58. This is an application of the distributive property of multiplication over subtraction, which in general form is expressed as a(b - c) = ab - ac. To perform the verification, we distribute the 27 to both 34 and 58 within the parentheses. Here is the step-by-step process:
- Multiply 27 by 34 to get 918.
- Multiply 27 by 58 to get 1566.
- Subtract the second product from the first to verify the equation: 918 - 1566 equals -648.
- So, 27 multiplied by (34 - 58) also equals -648, verifying the original equation as correct.
This shows the use of the distributive property and ensures that both the left and right sides of the equation are equivalent.