Question

Разложите на множители а)4x-xy^2= б)4a^4-25b^2-2ax^2b= в)8+x^3+2x^4+16x= памогите пожалуйста

Answer 1

А) = х( 4 - у²)
б) = 
в) = ( 8 +  х³) + ( 2х^4 + 16x) + (8 + х²) + 2х( х³ +8) = ( х³ + 8)( 1 +2х)

Answer 2

Разложение на множители

а) 4x - xy^2

To factorize the expression 4x - xy^2, we can factor out the common factor of x from both terms:

4x - xy^2 = x(4 - y^2)

The expression can be further simplified by recognizing that (4 - y^2) is a difference of squares, which can be factored as (2 - y)(2 + y):

4x - xy^2 = x(2 - y)(2 + y)

Therefore, the expression 4x - xy^2 can be factored as x(2 - y)(2 + y).

б) 4a^4 - 25b^2 - 2ax^2b

To factorize the expression 4a^4 - 25b^2 - 2ax^2b, we can look for common factors among the terms. In this case, there are no common factors among all three terms.

However, we can factor out a common factor of (2a^2) from the first and third terms, and a common factor of 5b from the second term:

4a^4 - 25b^2 - 2ax^2b = 2a^2(2a^2 - x^2b) - 5b(5b + 2ax^2)

The expression can be further simplified by recognizing that (2a^2 - x^2b) is a difference of squares, which can be factored as (sqrt(2)a - sqrt(x)b)(sqrt(2)a + sqrt(x)b):

4a^4 - 25b^2 - 2ax^2b = 2a^2(sqrt(2)a - sqrt(x)b)(sqrt(2)a + sqrt(x)b) - 5b(5b + 2ax^2)

Therefore, the expression 4a^4 - 25b^2 - 2ax^2b can be factored as 2a^2(sqrt(2)a - sqrt(x)b)(sqrt(2)a + sqrt(x)b) - 5b(5b + 2ax^2).

в) 8 + x^3 + 2x^4 + 16x

To factorize the expression 8 + x^3 + 2x^4 + 16x, we can look for common factors among the terms. In this case, there are no common factors among all four terms.

However, we can factor out a common factor of 8 from the first and fourth terms, and a common factor of x from the second and third terms:

8 + x^3 + 2x^4 + 16x = 8(1 + x^3/8 + 2x^4/8 + 2x)

The expression can be further simplified by factoring out an x from the second and third terms:

8 + x^3 + 2x^4 + 16x = 8(1 + x^3/8 + 2x^4/8 + 2x) = 8(1 + x^3/8 + x^3/4 + 2x)

Now, we can combine the terms with x^3:

8 + x^3 + 2x^4 + 16x = 8(1 + (x^3/8 + x^3/4) + 2x)

Simplifying further:

8 + x^3 + 2x^4 + 16x = 8(1 + (2x^3/8) + 2x)

Finally, we can factor out a common factor of 2x from the terms inside the parentheses:

8 + x^3 + 2x^4 + 16x = 8(1 + (2x^3/8) + 2x) = 8(1 + x^3/4 + 2x)

Therefore, the expression 8 + x^3 + 2x^4 + 16x can be factored as 8(1 + x^3/4 + 2x).

I hope this helps! Let me know if you have any further questions.