the simplest form of ac+ad+bc+bd is
Answers
Answer:
The simplest form is-:
(a+b) (c+d)
Answer:
How do you demonstrate that (a+b)(c+d)=ac+ad+bc+bd ?
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shows one way if you are working in a group which has the commutative property for multiplication and the left-distributive property for multiplication over addition.
However, if we assume we have both the left-distributive and right-distributive properties, we do not need to assume commutativity at all. This is important since one of the most important algebraic structures for linear algebra, the matrix, has these properties but multiplication over matrices is not commutative.
(a+b)(c+d)=a(c+d)+b(c+d)=ac+ad+b(c+d)=ac+ad+bc+bd .
Much shorter, and no commutation needed. We only need right-distributivity as well as left-distributivity.
Coincidentally, if we have commutativity as well as left-distributivity, we necessarily also have right-distributivity (as shown by but the converse does not hold (for example addition and multiplication of matrices).