Question

Упростите по формулам сокращённого умножения

Answer 1

(х + 1)^2 - 1 - (х - 1)^2 = х^2 + 2х + 1 - 1 - ( х^2 - 2х +1) = х ^2 + 2х - х^2 + 2х - 1 = 4х - 1

Answer 2

(х+1)² -1- (х-1)²=(х²+2х+1)-1-(х²-2х+1)=х²+2х+1-1- х²+2х-1 =4х-1

Answer 3

Simplifying Using the Formulas of Polynomial Factorization

To simplify using the formulas of polynomial factorization, we can apply various identities and rules. Let's go through some examples and simplify them using the given formulas.

1. (a, b)^2 - (a - b)^2: - The formula for this expression is: (a, b)^2 - (a - b)^2 = 4ab. - Applying the formula, we get: 4ab.

2. (x + y)^2 - 3xy(x + y): - The formula for this expression is: (x + y)^2 - 3xy(x + y) = x^2. - Applying the formula, we get: x^2.

3. (a - b)^2 + 3ab(a - b): - The formula for this expression is: (a - b)^2 + 3ab(a - b) = a^2 - b^2. - Applying the formula, we get: a^2 - b^2.

4. (3m - n)^2 - (n + 3m)^2: - The formula for this expression is: (3m - n)^2 - (n + 3m)^2 = -6m^2n - 2n^3. - Applying the formula, we get: -6m^2n - 2n^3.

5. 3ab(a + b) - (a + b)^2: - The formula for this expression is: 3ab(a + b) - (a + b)^2 = -a^2 - b^2. - Applying the formula, we get: -a^2 - b^2.

6. (m - n)^2 - (m - n)(m^2 + mn + n^2): - The formula for this expression is: (m - n)^2 - (m - n)(m^2 + mn + n^2) = -3m^2n + 3mn^2. - Applying the formula, we get: -3m^2n + 3mn^2.

These formulas and their applications help simplify expressions involving polynomial factorization. If you have more specific examples or further questions, feel free to ask!