Question

1) a^7+ab^6 2) x^8 - y^8 3) c^6-1

Answer 1

Решение..................

Answer 2

1) a^7 + ab^6 The expression a^7 + ab^6 can be simplified by factoring out the common term.

First, factor out the common term "a^6" from both terms: a^7 + ab^6 = a^6 * a + a^6 * b^6 Now, we have: a^6(a + b^6)

So, the simplified form of the expression is a^6(a + b^6).

2) x^8 - y^8 The expression x^8 - y^8 is a difference of squares and can be factored using the difference of squares formula: x^8 - y^8 = (x^4)^2 - (y^4)^2 Using the difference of squares formula (a^2 - b^2 = (a + b)(a - b)), we get: x^8 - y^8 = (x^4 + y^4)(x^4 - y^4)

Now, the expression is factored as: (x^4 + y^4)(x^4 - y^4).

3) c^6 - 1 The expression c^6 - 1 can be factored as a difference of squares: c^6 - 1 = (c^3)^2 - 1^2 Using the difference of squares formula, we get: c^6 - 1 = (c^3 + 1)(c^3 - 1)

So, the simplified form of the expression is (c^3 + 1)(c^3 - 1).

These are the detailed simplifications of the given expressions. If you have any more questions or need further assistance, feel free to ask!