Sure, let's verify the given expression step-by-step and identify the property used.
We start with the expression:
[tex]\[ (-3) \times [(-7) + (-5)] \][/tex]
First, let's simplify inside the brackets:
[tex]\[ (-7) + (-5) = -12 \][/tex]
So the expression becomes:
[tex]\[ (-3) \times (-12) \][/tex]
When we multiply these two numbers:
[tex]\[ (-3) \times (-12) = 36 \][/tex]
Now let's evaluate the right-hand side of the equation:
[tex]\[ [(-3) \times (-7)] + [(-3) \times (-5)] \][/tex]
First, calculate each term inside the brackets separately:
[tex]\[ (-3) \times (-7) = 21 \][/tex]
[tex]\[ (-3) \times (-5) = 15 \][/tex]
Now, add these two results together:
[tex]\[ 21 + 15 = 36 \][/tex]
Thus, the right-hand side becomes:
[tex]\[ 36 \][/tex]
We have found that the left-hand side is:
[tex]\[ 36 \][/tex]
And the right-hand side is:
[tex]\[ 36 \][/tex]
Therefore, both sides of the equation are equal:
[tex]\[ (-3) \times [(-7) + (-5)] = 36 \][/tex]
[tex]\[ [(-3) \times (-7)] + [(-3) \times (-5)] = 36 \][/tex]
Both sides equal 36, verifying the given expression.
The property used to verify this equation is the Distributive Property. This property states that [tex]\( a \times (b + c) = (a \times b) + (a \times c) \)[/tex], where [tex]\( a, b, \)[/tex] and [tex]\( c \)[/tex] are any real numbers.
