Sure, let's simplify the equation [tex]\( 4(10 + 5) = 6(12 - 2) \)[/tex] step-by-step by applying the distributive property.
Step 1: Apply the distributive property to both sides of the equation.
- For the left side [tex]\( 4(10 + 5) \)[/tex]:
[tex]\[
4 \times 10 + 4 \times 5
\][/tex]
This simplifies to:
[tex]\[
40 + 20
\][/tex]
- For the right side [tex]\( 6(12 - 2) \)[/tex]:
[tex]\[
6 \times 12 - 6 \times 2
\][/tex]
This simplifies to:
[tex]\[
72 - 12
\][/tex]
Now, let's rewrite both sides of the equation:
[tex]\[
40 + 20 = 72 - 12
\][/tex]
So the correct way to rewrite the equation [tex]\( 4(10 + 5) = 6(12 - 2) \)[/tex] using the distributive property is:
[tex]\[
40 + 20 = 72 - 12
\][/tex]
Therefore, the correct choice from the provided options is:
[tex]\[
40 + 20 = 72 - 12
\][/tex]
