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3 years ago

Because of the commutative property of multiplication, it is true that

Mathematics

1 answer:

rewona [7]3 years ago

3 0

Answer:

It is Commutative

Step-by-step explanation:

An operation ∆ is said to be Commutative if a∆b=b∆a ∀ a,b ∈ ℝ.

Given the operation ∆ defined by:

a∆b=a X b

$a=\frac{3}{4}, b=4$

a∆b= $\frac{3}{4}X4$

$=\frac{3X4}{4}$ =3

Similarly, for the right hand side.

$(\frac{4}{3})^{-1}=\frac{3}{4}$

Therefore:

b∆a= $4X \frac{3}{4}$

$=\frac{4X3}{4}$ =3

These are the two ways of solving this problem and we have in fact shown that the operation is commutative as:

a∆b=b∆a=3

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Which of the following expressions is equivalent to a3 + b3?

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ANSWER
${a}^{3} + {b}^{3} = (a + b)( {a}^{2 } - ab + {b}^{2} )$

EXPLANATION

To find the expression that is equivalent to
${a}^{3} + {b}^{3}$
we must first expand
${(a + b)}^{3}$
Then we rearrange to find the required expression.

So let's get started.

${(a + b)}^{3} = (a + b) {(a + b)}^{2}$

We expand the parenthesis on the right hand side to get,

${(a + b)}^{3} = (a + b) ( {a}^{2} + 2ab + {b}^{2} )$

We expand again to obtain,

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Let us group the cubed terms on the right hand side to get,

${(a + b)}^{3} = {a}^{3} + {b}^{3} + 3 {a}^{2}b + 3a {b}^{2}$

${(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab (a+ b)$

We make the cubed terms the subject,

${(a + b)}^{3} - 3ab (a+ b) = {a}^{3} + {b}^{3}$

We factor to get,

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