Final answer:
The expression (x+5)² -(x-5)² is always divisible by 4.
Step-by-step explanation:
Divisibility is a mathematical property that describes whether one number can be evenly divided by another. In other words, a number a is divisible by another number b if the division a÷b results in a quotient without any remainder. If there is no remainder, we say that a is divisible by b, or that b is a divisor of a.To show that the expression (x+5)² -(x-5)² is always divisible by 4, we can simplify the expression and factor it.
(x+5)² -(x-5)²
= [(x+5)+(x-5)][(x+5)-(x-5)]
= [2x][10]
= 20x
Since 20x is a multiple of 4 for any value of x, we can conclude that the expression (x+5)² -(x-5)² is always divisible by 4.