Question

3) -3m²-6mn-3n²4) 3ab-21b+6a-425) 16-x⁴Разложить на множители​

Answer 1

Объяснение:

3)-(m²+2mn+m)²

-3(m+n)²

4)3(ab-7b+2a-14)

3(b(a-7)+2(a-7))

3(a-7)(b+2)

5)(4-x²)(4×x²)

(2-x)(2+x)(4+x²)

Answer 2

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

1. Factorizing -3m² - 6mn - 3n²:

Step 1: Factor out the common factor, which is -3. -3(m² + 2mn + n²)

Step 2: Factorize the quadratic expression m² + 2mn + n² as a perfect square. -3(m + n)²

So, the fully factored expression is -3(m + n)².

2. Factorizing 3ab - 21b + 6a - 42:

Step 1: Factor out the common factor, which is 3. 3(ab - 7b + 2a - 14)

Step 2: Group the terms and factorize by common factors. 3[a(b - 7) + 2(a - 7)]

Step 3: Factor out the common factor inside the brackets. 3(a - 7)(b - 2)

So, the fully factored expression is 3(a - 7)(b - 2).

3. Factorizing 16 - x⁴:

Step 1: This expression is a difference of squares. (4 + x²)(4 - x²)

Step 2: The second factor is a difference of squares again. (4 + x²)(2 + x)(2 - x)

So, the fully factored expression is (4 + x²)(2 + x)(2 - x).

These are the factored forms of the given expressions.