Final answer:
The given expressions have been verified using the distributive property for multiplication over addition in part a, confirming that 15 times (8+(-2)) equals 90, and properties of addition for part b, confirming that a-(-b) equals a+b when a = 28 and b = 81.
Step-by-step explanation:
Verification of Algebraic Expressions
To verify the expressions given in parts a and b, we need to use the distributive property for part a and the properties of addition for part b.
Part a: We will verify if (15 times (8+(-2)) equals 15 times 8 + 15 times (-2)). According to the distributive property of multiplication over addition, we have:
15 × (8 + (-2)) = 15 × 8 + 15 × (-2).
This simplifies to: 120 + (-30).
So the final answer is 90, which verifies the expression as true.
Part b: For the values given, a = 28 and b = 81, the expression a - (-b) = a + b holds true because when subtracting a negative number, it is equivalent to addition. Therefore:
a - (-b) becomes 28 + 81.
That simplifies to 109, verifying the expression as true.
Through these examples, we see that arithmetic operations and their properties, like the distribution of multiplication over addition or subtraction and the rules for adding numbers with different signs, are consistent and can be applied to verify such equations.