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Q3. Verify the following expression and write the name of the property used.

[tex]\[ (-3) \times [(-7) + (-5)] = [(-3) \times (-7)] + [(-3) \times (-5)] \][/tex]

Sagot :

GinnyAnsweridn
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.
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