Question

Помогите решить!алг. 7 кл. Разложите на множители многочлен: 3ab-b(в квадрате)+3a(в квадрате)-ab=? всем спасибо!!!!!

Answer 1

3ab-b²+3a²-ab=3a(b+a)-b(b+a)=(b+a)(3a-b)

Answer 2

Factoring the Polynomial

To factor the polynomial 3ab - b^2 + 3a^2 - ab, we can look for common factors and then use the distributive property to factor out the common terms.

Let's break down the polynomial step by step:

1. 3ab - b^2 + 3a^2 - ab

We can group the terms with common factors:

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

Simplifying further:

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

2. Now, let's focus on factoring the expression (3a^2 - b^2).

This expression is a difference of squares, which can be factored as:

(3a + b)(3a - b)

3. Combining this factorization with the previous step, we have:

2ab + (3a + b)(3a - b)

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

Please let me know if you need any further assistance!