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Arturiano [62]
3 years ago
6

Which expression is a sum of cubes?

Mathematics
2 answers:
valkas [14]3 years ago
8 0

<u>ANSWER</u>

- 27 {a}^{3}  {b}^{6}  + 8 {a}^{9}  {b}^{12}

<u>EXPLANATION</u>

When we can write an expression in the form

{(x)}^{3}  +  {(y)}^{3}

then it is a sum of cubes.

To write a given sum as sum of cubes, then the coefficients of the terms should cube be numbers and the exponents of any power should be a multiple of 3.

This tells us that the first option will be the best choice.

- 27 {a}^{3}  {b}^{6}  + 8 {a}^{9}  {b}^{12}

We can rewrite this as:

{ (- 3)}^{3}  {a}^{3}  {b}^{2 \times 3}  +  {2}^{3}  {a}^{3 \times 3}  {b}^{4 \times 3}

We apply this property of exponents:

({a}^{m} )^{n} =  {a}^{mn}

This gives us

{( - 3a {b}^{2}) }^{3}  +  {(2{a}^{3} {b}^{4}  })^{3}

Therefore the correct option is A

vovangra [49]3 years ago
5 0

Answer:

-27a³b⁶+ 8a⁹b¹²

Step-by-step explanation:

In the expression above -27 is a perfect cube of -3, 8 is a perfect cube of 2.

The exponents of a and b in both terms in the expression are divisible by 3.

The cube root of x, that is ∛xⁿ=x∧(n/3) where n is an integer.

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every value of the domain only has one corresponding value

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4 years ago
Find the geometric mean between each pair of numbers. 28 and 7
Viktor [21]
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7 0
4 years ago
Need Help With This​
podryga [215]

Answer:

4n-13

Step-by-step explanation:

Terms= -13 (constant)

Coefficient= 3, -5, 6

Like term= 3n, -5n, 6n

3n-13-5n+6n

3n+6n-5n-13

9n-5n-13

4n-13

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4 0
3 years ago
I require assistance please. ​
Zolol [24]

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3 0
3 years ago
Claire's music playlist contains songs she bought and songs her mother bought. The ratio of her songs to her mother's songs is 3
Vsevolod [243]

Answer:

B.

Step-by-step explanation:

The ratio of Claire's songs to her mother's songs = 3 : 2

A.

3 : 2 = 3/2

9 : 6 = 9/6 = 3/2

12 : 10 = 12/10 = 6/5

B.

3 : 2 = 3/2

6 : 4 = 6/4 = 3/2

15 : 10 = 15/10 = 3/2

C.

3 : 2 = 3/2

4 : 3 = 4/3

5 : 4 = 5/4

D.

3 : 2 = 3/2

4 : 6 = 4/6 = 2/3

20 : 30 = 20/30 = 2/3

The table which shows the correct ratio and two equivalent ratios is B

7 0
3 years ago
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