Question

1) (x²+b)(x²+2b) = 2) (2m+n²)(2n-m²) = 3) (n+2m)(n-2m) = 4) (x+1)(x²-2x-1) =

Answer 1

1) x^4 3bx^2+2b^2;
2)4mn-2m^3-m^2n^2+2n^3;
3)n^2-4m^2;
4)x^3-2x^2-x-x^2-2x-1=-3x^2+x^3-3x-1.
(Знак ^ означает степень, например, 2x^2 означает два икс в квадрате и т.д.)

Answer 2

Let's simplify each of the given expressions:

1. (x²+b)(x²+2b)

Expanding this expression using the distributive property, we get:

x² * x² + x² * 2b + b * x² + b * 2b

Combining like terms, we have:

x^4 + 2bx^2 + bx^2 + 2b^2

Simplifying further:

x^4 + (2b + b)x^2 + 2b^2

Final simplified expression: x^4 + 3bx^2 + 2b^2

2. (2m+n²)(2n-m²)

Expanding this expression:

(2m)(2n) + (2m)(-m²) + (n²)(2n) + (n²)(-m²)

Simplifying each term:

4mn - 2m³ + 2n³ - m²n²

Final simplified expression: -2m³ + 2n³ + 4mn - m²n²

3. (n+2m)(n-2m)

Using the difference of squares formula:

(n)² - (2m)²

Simplifying further:

n² - 4m²

Final simplified expression: n² - 4m²

4. (x+1)(x²-2x-1)

Expanding this expression:

(x)(x²) + (x)(-2x) + (x)(-1) + (1)(x²) + (1)(-2x) + (1)(-1)

Simplifying each term:

x³ - 2x² - x + x² - 2x - 1

Combining like terms:

x³ - x² - 3x - 1

Final simplified expression: x³ - x² - 3x - 1