Question

Разложите многочлен на множители A) 3a-6b+ab-2b^2 B) 4a^2 - q C) y^3+18y^2+81y ОЧЕНЬ НУЖНО, ЧЕТВЕРТНАЯ

Answer 1

A) $3a-6b+ab-2b^2=3(a-2b)+b(a-2b)=(3+b)(a-2b)$

b) $4a^2-q=(2a- \sqrt{q} )(2a+ \sqrt{q} )$

c) $y^3+18y^2+81y=y(y^2+18y+81)=y(y+9)^2$

Answer 2

Разложение многочлена на множители

A) 3a - 6b + ab - 2b^2

To factorize this polynomial, we can look for common factors among the terms. In this case, we can see that the common factor is (a - 2b):

3a - 6b + ab - 2b^2 = (a - 2b)(3 + b)

Therefore, the factored form of the polynomial is (a - 2b)(3 + b).

B) 4a^2 - q

The polynomial 4a^2 - q does not have any common factors that can be factored out. So, it remains as it is.

C) y^3 + 18y^2 + 81y

To factorize this polynomial, we can look for common factors among the terms. In this case, we can see that the common factor is y:

y^3 + 18y^2 + 81y = y(y^2 + 18y + 81)

Now, let's focus on the quadratic term y^2 + 18y + 81. We can factorize it further by looking for two numbers whose product is 81 and whose sum is 18. These numbers are 9 and 9:

y^2 + 18y + 81 = (y + 9)(y + 9) = (y + 9)^2

Therefore, the factored form of the polynomial y^3 + 18y^2 + 81y is y(y + 9)^2.

Вывод

A) 3a - 6b + ab - 2b^2 = (a - 2b)(3 + b) B) 4a^2 - q (нельзя разложить на множители) C) y^3 + 18y^2 + 81y = y(y + 9)^2

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