Pls help ASAP!
You will have to determine if the statement is true or false. If it's false you will explain your reasoning.
For all real numbers a and b, 2a • b = a² + b²
The statement is false.
In order for the statement to be true, the equation 2a • b = a² + b² should hold for all real numbers a and b.
Let's consider a counterexample to show that the statement is false.
If we choose a = 0 and b = 1, then the left-hand side of the equation becomes 2(0) • 1 = 0, while the right-hand side becomes 0² + 1² = 1. Since 0 does not equal 1, the equation does not hold true.
Therefore, the statement is false.
To determine if the statement is true or false, we can substitute some real numbers for a and b and check if the equation holds true.
Let's choose a = 2 and b = 3.
According to the statement, 2a • b = a² + b².
Substituting the values, we have:
2(2) • 3 = 2² + 3².
4 • 3 = 4 + 9.
12 = 13.
Since 12 is not equal to 13, the equation does not hold true. Therefore, the statement is FALSE.
The reasoning behind this is that the equation 2a • b = a² + b² is not a correct representation of the property of multiplying two numbers by two.