Question

Factor: 3x4y3 – 48y3.​

Answer 1

Решение на фоторафии.......

Answer 2

To factor the expression 3x^4y^3 - 48y^3, we can first factor out the common term, which is y^3:

y^3(3x^4 - 48)

Now, let's focus on factoring the expression within the parentheses, 3x^4 - 48. We can see that both terms have a common factor of 3, so let's factor that out:

3(x^4 - 16)

Now, notice that x^4 - 16 is a difference of squares (x^2)^2 - 4^2. This can be factored further using the difference of squares formula: a^2 - b^2 = (a + b)(a - b):

3((x^2 + 4)(x^2 - 4))

We can further factor x^2 - 4 as another difference of squares: (x^2 - 2^2):

3((x^2 + 4)(x + 2)(x - 2))

So, the fully factored expression is:

3y^3(x^2 + 4)(x + 2)(x - 2)