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4 years ago

Enter the correct answer in the box. Use the sum of cubes identity to find the factors of the expression 8x^6 + 27y^3

Mathematics

2 answers:

Dovator [93]4 years ago

4 0

Answer:

(2x^2 + 3y)(4x^4 - 6x^2y + 9y^2).

Step-by-step explanation:

a^3 + b^3 = (a + b)(a^2 - ab + b^2) is the identity.

Comparing this with the sum in the question:

a = 2x^2 and b = 3y so we have:

8x^6 + 27y^3 = (2x^2 + 3y)(4x^4 - 2x^2*3y + 9y^2)

= (2x^2 + 3y)(4x^4 - 6x^2y + 9y^2).

KengaRu [80]4 years ago

3 0

I need this answer too

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WILL GIVE BRAINLIEST! NEED QUICK HELP ASAP! Photo added! least common denominator x^3/x^2+4x+4 and -9/x^2+5x+6

Oksanka [162]

The denominator( s ) we are given are $x^2 + 4x + 4$ , and . The first thing we want to do is factor the expressions, to make this easier -

$x^2 + 4x + 4$

This expression is a perfect square, as ( x )^2 = x^2, ( 2 )^2 = 4, 2 * ( x ) * ( 2 ) = 4x. Thus, the simplified expression should be the following -

$( x + 2 )^2$

The other expression is, on the other hand, not a perfect square so we must break this expression into groups and attempt factorization -

$x^2 + 5x + 6,\\\left(x^2+2x\right)+\left(3x+6\right),\\x\left(x+2\right)+3\left(x+2\right),\\\left(x+2\right)\left(x+3\right)\\\\Factored Expression = \left(x+2\right)\left(x+3\right)$

Combining ( x + 2 )^2 and ( x + 2 )( x + 3 ), the expression that contains factors of each is ( x + 2 )^2 * ( x + 3 ), or in other words the LCM.

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3 years ago

Which number line best shows how to solve -4-(-8)

Rama09 [41]

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3 years ago

Barney's Book Store currently has 2000 books in stock. There are 3 times as many non-fiction books as fiction books. Determine t

xxMikexx [17]

Answer:

There are 1500 non fiction books and 500 fiction books currently in the store.

Step-by-step explanation:

Given:

Total Number of books = 2000

Let the number of fiction books be 'x'.

Now given:

There are 3 times as many non-fiction books as fiction books.

Number of non fiction books = $3x$

We need to find the number of non-fiction and fiction books.

Solution:

Now we know that;

Total Number of books is equal to sum of the number of non-fiction and fiction books.

framing in equation form we get;

$x+3x=2000\\\\4x=2000$

Dividing both side by 4 we get;

$\frac{4x}{4}=\frac{2000}{4}\\\\x= 500\ books$

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3 years ago

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3 years ago

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ivann1987 [24]

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First we will find LCM for first two numbers ( 16 and24 ).

Step 1: Find the GCD (Greatest Common Divisor ) of 16 and 24 which is 8.

Step 2: Multiply the numbers 16 and 24 together ( 16 * 24 = 384 )

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So, the LCM of 16 and 24 is 48.

Now we will find the LCM of above result (48) and third number ( 40 ) using the same procedure.

The result of this part is 240

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