Question

PROVE THAT A*(B-C)=(A*B)-(A*C)

Answer 1

A(B-C) = (A*B)-(A*C)
AB-AC = AB-AC 
Therefore LHS = RHS

Answer 2

Answer:

The equality $A * (B - C)=$ $(A * B) - (A * C)$ is proved.

Step-by-step explanation:

Distributive property over subtraction:-

• The binary operation of a number by the difference of two other numbers is equal to the binary operation of the products of the distributed number.
• Mathematically, $a * (b - c) = (a * b) - (a * c)$.

Step 1 of 1

To prove:-

$A * (B - C)=$  $(A * B) - (A * C)$

Consider the left-hand side of the given equality as follows:

A * (B - C)

Using the distributive property over subtraction, we get

A * B - A * C

$(A * B) - (A * C)$

This implies, LHS $=$ $(A * B) - (A * C)$

And the RHS $=$ $(A * B) - (A * C)$

Thus, the expression on the left-hand side is equal to the expression on the right-hand side.

LHS = RHS

⇒ $A * (B - C)=$ $(A * B) - (A * C)$

Hence proved.

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