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Tresset [83]
3 years ago
9

The following is a proof of the algebraic equivalency of (2x)³ and 8x³. Fill in each of the blanks with either the statement com

mutative property or associative property.
(2x)³ =2x∙2x∙2x
=2(x×2)(x×2)x ___________________
=2(2x)(2x)x ___________________
=2∙2(x×2)x∙x ___________________
=2∙2(2x)x∙x ___________________
=(2∙2∙2)(x∙x∙x) ___________________
=8x³
Mathematics
2 answers:
Wittaler [7]3 years ago
5 0

You're using the commutative property when you swap the order of factors in a multiplication:

a\cdot b = b\cdot a

and you use the associative property when you regroup the products of more than 2 factors in a different way:

(a\cdot b)\cdot c = a\cdot (b\cdot c)

So, you're constantly alternating between associative and commutative. Try to see which property you're using in the first step, and then keep alternating between the two!

german3 years ago
4 0

Answer:

The reasons for each statement are show below.

Step-by-step explanation:

We need to prove (2x)³ is equivalent to 8x³.

Commutative property: According to the commutative property of multiplication

a\cdot b=b\cdot a

Associative property: According to the associative property of multiplication

a\cdot (b\cdot c)=(a\cdot b)\cdot c

The given expression (2x)³ can be written as

(2x)^3=(2x)\cdot (2x)\cdot (2x)

(2x)^3=2(x\cdot 2)(x\cdot 2)x               (Associative property)

(2x)^3=2(2x)(2x)x                           (Commutative property)

(2x)^3=(2\cdot 2)(x\cdot 2)(x\cdot x)               (Associative property)

(2x)^3=(2\cdot 2)(2\cdot x)(x\cdot x)                           (Commutative property)

(2x)^3=(2\cdot 2\cdot 2)(x\cdot x\cdot x)               (Associative property)

(2x)^3=8x^3

Hence proved.

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