Question

1) 1-4a-b^2+4ab^2 2) 2a-b^2+2ab-b разложить на множители

Answer 1

1)1-4a-b^2+4ab^2=(4а-1)(b-1)(b+1);
2)2a-b^2+2ab-b =(b+1)(2a-b).

Answer 2

To factorize the given expressions, let's take them one by one:

1. Factorizing the expression 1-4a-b^2+4ab^2:

First, we can try to group the terms in pairs:

1 - 4a - b^2 + 4ab^2

= (1 - 4a) + (-b^2 + 4ab^2)

Now, we can factor out common terms from each pair:

= 1(1 - 4a) + b^2(-1 + 4a)

Now, we have a difference of squares in the second part, which can be factored:

= 1(1 - 4a) + b^2(4a - 1)

Finally, we can factor out the common factor (1 - 4a):

= (1 - 4a)(1 + b^2)

So, the factored expression is: (1 - 4a)(1 + b^2)

2. Factorizing the expression 2a - b^2 + 2ab - b:

There are no common terms to factor out in this expression, so we need to find common factors among the terms:

2a - b^2 + 2ab - b

Now, let's rearrange the terms:

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

Now, we can factor out common terms from each pair:

= 2a(1 + b) - b(b + 1)

Notice that we have a common factor (1 + b) in both terms. So, we can factor it out:

= (1 + b)(2a - b)

So, the factored expression is: (1 + b)(2a - b)