Question

Как разложить многочелен на множители 9a²-6a+1-4b²

Answer 1

9a² -6a +1 =(3a -1)² ;

9a²-6a+1 -4b² =(3a -1)²-4b²
тогда по формуле
a² -b² =(a -b)(a +b)
пусть 3a -1 =x

x² -4b² =(x -2b)(x +2b) = (3a -1 -2b)(3a -1 +2b)

Answer 2

Factoring the Polynomial 9a² - 6a + 1 - 4b²

To factor the given polynomial 9a² - 6a + 1 - 4b², we can use the method of factoring by grouping.

First, let's factor the polynomial by grouping the terms:

1. Factor by Grouping: - Group the terms in pairs: (9a² - 6a) and (1 - 4b²). - Factor out the greatest common factor from each pair.

The greatest common factor for the first pair is 3a, and for the second pair, it's 1.

Factoring the first pair, we get: 3a(3a - 2). Factoring the second pair, we get: 1 - 4b².

So, the factored expression becomes: 3a(3a - 2) + (1 - 4b²).

2. Further Factoring: - Now, we can further factor the expression 1 - 4b² using the difference of squares formula.

The difference of squares formula states that a² - b² = (a + b)(a - b).

Applying the difference of squares formula to 1 - 4b², we get: (1 + 2b)(1 - 2b).

So, the fully factored expression becomes: 3a(3a - 2) + (1 + 2b)(1 - 2b).

Therefore, the factored form of the given polynomial 9a² - 6a + 1 - 4b² is 3a(3a - 2) + (1 + 2b)(1 - 2b).