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3 years ago

Factories (a+b)^3+8c^3

Mathematics

1 answer:

Rom4ik [11]3 years ago

8 0

Answer:

(a + b + 2c)(a² + 2ab + b² - 2ac - 2bc + 4c²)

Step-by-step explanation:

Given

(a + b)³ + 8c³ ← this is a sum of cubes and factors in general as

a³ + b³ = (a + b)(a² - ab + b²)

Thus

(a + b)³ + 8c³

= (a + b)³ + (2c)³

= (a + b + 2c)( (a + b)² - 2c(a + b) + (2c)² )

= (a + b + 2c)(a² + 2ab + b² - 2ac - 2bc + 4c²)

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kumpel [21]

Answer:

Ball hits the ground after 4.5 sec

Step-by-step explanation:

Let a -1, so that the leading coefficient is positive

So our quadratic is

$-1 \times (16t^2 +18t -405)$

The key coefficients of two binomial variables can be 1 and 16, or 2 and 8, or 4 and 4, for the leading coefficient of 16.

Yet they can't actually be 4 and 4 because the linear (x) term coefficient has to be a multiple of 4, which it isn't and leading coefficients 1 and 16 on the binomial factors is not likely.

So, 2 and 8 taken as the leading coefficients of two binomial factors.

For constant 405, possible factorizations are $(81\times 5, 27 \times 15, 9 \times 45).$

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Taking first factor, thus we find negative value for given time t. But second time equivalent to zero gives the value of 4.5 for t

Thus ball hits the ground after 4.5 sec

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The graph of function g is a vertical stretch of the graph of function f by a factor of 3. Which equation describes function g

anyanavicka [17]

Answer:

Step-by-step explanation:

A vertical stretch by a factor of k means that the point (x, y) on the graph of f (x) is transformed to the point (x, ky) on the graph of g(x), where k <1.

If k =1, then same graph we obtain and if k>1 we get a vertically shrink graph.

In our question, there is a vertical stretch of 3. This means new graph would have points as (x,y/3)

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