Mathematics: Two streaming video subscriptions services offer family plans with different monthly costs as shown in the ads below what do the two plans have in common how are they different when is movies4you a better deal than family stream movies4you $10 for first device plus additional $2 for each device family stream $12 flat rate for up to 4 devices additional fee of $1 for 5 or more devices

Two streaming video subscriptions services offer

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24.01.2023

1) The factorization is: 2a(a^2 + 2a + 4)

2) The factorization is: 6y^2(y - 7)(y + 7)

3) The factorization is: 5(x+5)^2

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To factor each expression, we apply the given concepts, that is, greatest common factor, difference of squares and perfect squares.

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Expression 1:

The expression is:

2a^3 + 4a^2 + 8a

First, we find the gcf of the numbers 2, 4 and 8, which is 2.

Of the exponents, the gcf between 3, 2 and 1 is 1, so:

$2a^3 + 4a^2 + 8a = 2a(\frac{2a^3}{2a} + \frac{4a^2}{2a} + \frac{8a}{2a}) = 2a(a^2 + 2a + 4)$

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Expression 2:

The expression is:

6y^4 - 294y^2

The gcf of 6 and 294 is 6.

The gcf of the exponents 2 and 4 is 4.

Thus:

$6y^4 - 294y^2 = 6y^2(\frac{6y^4}{6y^2} - \frac{294y^2}{6y^2}) = 6y^2(y^2 - 49)$

Then, applying the difference of squares:

y^2 - 49 = (y - 7)(y + 7)

Thus, the factored expression is:

6y^2(y^2 - 49) = 6y^2(y - 7)(y + 7)

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Expression 3:

The expression is:

5x^2 + 50x + 125

The gcf of the coefficients, 5, 50 and 125 is 5, so:

$5(\frac{5x^2}{5} + \frac{50x}{5} + \frac{125}{5}) = 5(x^2 + 10x + 25)$

Applying the perfect square, we get that:

x^2 + 10x + 25 = (x + 5)^2

Tus, the factored expression is:

5(x^2 + 10x + 25) = 5(x+5)^2

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