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Flauer [41]
3 years ago
15

How can sums and differences of cubes be identified for factoring?

Mathematics
1 answer:
Ad libitum [116K]3 years ago
7 0
The sum of cubes is given as:
a³ + b³ = (a + b)(a² - ab + b²)

Example for the sum of cubes:

64x³+y³ ⇒ This is the sum of cubes because each term; 64, x³, and y³ are cube numbers

By writing each term as an expression of cube numbers, we have:
(4x)³ + (y)³ ⇒ 64 is 4³
Use the factorization of the sum of cubes, we have:
(4x + y) ( (4x)²- 4xy + y²)
(4x + y) (16x² - 4xy + y²)

--------------------------------------------------------------------------------------------------------------

The difference of cubes can be factorized as:
(x³ - y³) = (x - y)(x² + xy + y²)

Example
(125x³ - 8y³) = (5x - 2y) ((5x)² + (5x)(2y) + (2y)²)
                     = (5x - 2y) (25x² + 10xy + 4y²)
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Answer:

x = -6.

Step-by-step explanation:

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3 years ago
Please help<br> log(8)10 - log(8) -3x = 1
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2 years ago
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The two problems are almost identical: you have to set up a system, and then solve it.

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So, we have the system

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For the second problem, let c and j be the number of pins knocked down by, respectively, Carrie and John. Just like before, we have the system

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And you can solve it in the very same way we solved the previous one.

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3 years ago
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