Chapter 9: Q. 34 (page 613)

Prove the distributive property:
$u \cdot (v + w) = u \cdot v + u \cdot w$

Short Answer

Expert verified

It is proved that $u \cdot (v + w) = u \cdot v + u \cdot w$ .

Step by step solution

Step 1. Given Information

We have to prove the distributive property $u \cdot (v + w) = u \cdot v + u \cdot w .$

Step 2. Proving

To prove the distributive property, let

$u = a i + b j v = x i + y j w = m i + n j$

Now, take L.H.S

role="math" localid="1646825259317" $u \cdot (v + w) = (a i + b j) \cdot (x i + y j + m i + n j) = (a i + b j) \cdot ((x + m) i + (y + n) j) = a (x + m) + b (y + n) = a x + a m + b y + b n = (a x + b y) + (a m + b n)$

R.H.S

$u \cdot v + u \cdot w = (a i + b j) \cdot (x i + y j) + (a i + b j) \cdot (m i + n j) = (ax + by) + (am + bn)$

L.H.S = R.H.S

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Prove the distributive property:
$u \cdot (v + w) = u \cdot v + u \cdot w$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Proving

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Prove the distributive property:u·(v+w)=u·v+u·w

Short Answer

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Most popular questions from this chapter

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Prove the distributive property:
$u \cdot (v + w) = u \cdot v + u \cdot w$