Question

Разложите на множители многочлены: 1) 12a 2 - 27b 22) 50m 2 - 8n 23) m - m 34) 3a 3 - 3a5) 8x 3 - 2x​

Answer 1

Ответ:

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Объяснение:

1)3(2a-3d)(2a+3d)

2)2(5m-2n)(5m+2n)

3)m(1-m)(1+m)

4)3a(a-1)(a+1)

5)2x(2x-1)(2x+1)

Answer 2

1. 12a^2 - 27b^2 can be factored as follows: 12a^2 - 27b^2 = 3(4a^2 - 9b^2)

Now, we recognize that 4a^2 - 9b^2 is a difference of squares, which can be factored as:

4a^2 - 9b^2 = (2a)^2 - (3b)^2 = (2a + 3b)(2a - 3b)

Therefore, the fully factored form of 12a^2 - 27b^2 is:

12a^2 - 27b^2 = 3(2a + 3b)(2a - 3b)

2. 50m^2 - 8n^2 cannot be factored further since there are no common factors between 50 and 8, as well as between m^2 and n^2. So the expression remains as is.

3. m - m^3 can be factored by taking out the common factor, which is m:

m - m^3 = m(1 - m^2)

Therefore, the fully factored form of m - m^3 is:

m - m^3 = m(1 - m^2)

4. 3a^3 - 3a^5 can be factored by taking out the common factor, which is 3a^3:

3a^3 - 3a^5 = 3a^3(1 - a^2)

Therefore, the fully factored form of 3a^3 - 3a^5 is:

3a^3 - 3a^5 = 3a^3(1 - a^2)

5. 8x^3 - 2x can be factored by taking out the common factor, which is 2x:

8x^3 - 2x = 2x(4x^2 - 1)

Now, we recognize that 4x^2 - 1 is a difference of squares, which can be factored as:

4x^2 - 1 = (2x)^2 - 1^2 = (2x + 1)(2x - 1)

Therefore, the fully factored form of 8x^3 - 2x is:

8x^3 - 2x = 2x(2x + 1)(2x - 1)