Question

Разложите на множители 1)b^2c-9c 2) 2a^2+12a+183) 25a-ab^24) 3a^2-6a+3

Answer 1

Разложение на множители:

1) b^2c - 9c + 2:

To factor this expression, we can look for common factors among the terms. In this case, we can factor out a common factor of c:

c(b^2 - 9) + 2

Next, we can factor the binomial b^2 - 9 using the difference of squares formula:

c((b)^2 - 3^2) + 2

Now, we have a difference of squares expression, which can be factored as:

c(b - 3)(b + 3) + 2

So, the expression b^2c - 9c + 2 can be factored as c(b - 3)(b + 3) + 2.

2) 2a^2 + 12a + 183:

To factor this expression, we can look for common factors among the terms. In this case, we can see that all the terms are divisible by 3:

3(2a^2 + 4a + 61)

Now, we need to factor the quadratic trinomial 2a^2 + 4a + 61. Since the coefficient of the leading term is 2, we need to find two numbers whose product is 2 * 61 = 122 and whose sum is 4. Unfortunately, there are no such two numbers, which means this expression cannot be factored further using real numbers.

So, the expression 2a^2 + 12a + 183 cannot be factored completely using real numbers.

3) 25a - ab^2 + 4:

To factor this expression, we can look for common factors among the terms. In this case, we can see that all the terms are divisible by a:

a(25 - b^2) + 4

Next, we can factor the binomial 25 - b^2 using the difference of squares formula:

a(5 - b)(5 + b) + 4

So, the expression 25a - ab^2 + 4 can be factored as a(5 - b)(5 + b) + 4.

4) 3a^2 - 6a + 3:

To factor this expression, we can look for common factors among the terms. In this case, we can see that all the terms are divisible by 3:

3(a^2 - 2a + 1)

Next, we can factor the quadratic trinomial a^2 - 2a + 1. This is a perfect square trinomial and can be factored as:

3(a - 1)(a - 1)

So, the expression 3a^2 - 6a + 3 can be factored as 3(a - 1)(a - 1).