Question

1. с^2-d^2 2. 49-x^2 3. x^2-y^2 4. a^2+2ax+x^2 5. y^2-2xy+x^2 6. 2x^2 y+4xy^2 7. x^2n-x^3n 8. y^(n+1) y^n

Answer 1

Ответ:

1) (c-d)(c+d)

2) (7-x)(7+x)

3) (x-y)(x+y)

4) (a+x)²

5) (y-x)²

6) 2xy(x+2y)

7)  nx²(1-x)

8) y²ⁿ+1

Answer 2

It looks like you've listed various algebraic expressions. Let's go through each of them:

1. с^2 - d^2: This is the difference of squares and can be factored as (с + d)(с - d).

2. 49 - x^2: This is another difference of squares and can be factored as (7 + x)(7 - x).

3. x^2 - y^2: This is a difference of squares and can be factored as (x + y)(x - y).

4. a^2 + 2ax + x^2: This is a perfect square trinomial and can be factored as (a + x)^2.

5. y^2 - 2xy + x^2: This is another perfect square trinomial and can be factored as (y - x)^2.

6. 2x^2y + 4xy^2: This expression doesn't seem to be factorable further without more context or specific instructions.

7. x^(2n) - x^(3n): This can be factored as x^(2n)(1 - x^n), which is a common factor for both terms.

8. y^(n+1) y^n: This is just y^(2n + 1), which is the product of y raised to the power of (n + 1) and y raised to the power of n.

Remember that factoring can involve various techniques, and the expressions might be further factorable if there are specific instructions or relationships provided.