Sure, let's verify each part step-by-step.
### Part (i)
We need to verify that:
[tex]\[
(-20) \times [13 + (-3)] = [(-20) \times 13] + [(-20) \times (-3)]
\][/tex]
First, let's calculate the left-hand side:
1. Compute the expression inside the parentheses:
[tex]\[
13 + (-3) = 10
\][/tex]
2. Multiply by -20:
[tex]\[
(-20) \times 10 = -200
\][/tex]
So the left-hand side is [tex]\(-200\)[/tex].
Next, let's calculate the right-hand side:
1. Multiply -20 by 13:
[tex]\[
(-20) \times 13 = -260
\][/tex]
2. Multiply -20 by -3:
[tex]\[
(-20) \times (-3) = 60
\][/tex]
3. Add the two results:
[tex]\[
-260 + 60 = -200
\][/tex]
Therefore, the right-hand side is also [tex]\(-200\)[/tex].
Since the left-hand side equals the right-hand side ([tex]\(-200 = -200\)[/tex]), the verification holds true for part (i).
### Part (ii)
We need to verify that:
[tex]\[
25 \times [7 + (-3)] = [25 \times 7] + [25 \times (-3)]
\][/tex]
First, let's calculate the left-hand side:
1. Compute the expression inside the parentheses:
[tex]\[
7 + (-3) = 4
\][/tex]
2. Multiply by 25:
[tex]\[
25 \times 4 = 100
\][/tex]
So the left-hand side is [tex]\(100\)[/tex].
Next, let's calculate the right-hand side:
1. Multiply 25 by 7:
[tex]\[
25 \times 7 = 175
\][/tex]
2. Multiply 25 by -3:
[tex]\[
25 \times (-3) = -75
\][/tex]
3. Add the two results:
[tex]\[
175 + (-75) = 100
\][/tex]
Therefore, the right-hand side is also [tex]\(100\)[/tex].
Since the left-hand side equals the right-hand side ([tex]\(100 = 100\)[/tex]), the verification holds true for part (ii).
In both cases, the given equalities are verified to be true.
