Question

Пользуясь тождеством a²-b²=(a+b)(a-b) разложить на множетели 1) a½-b½ 2) a⅓-b⅓ 3) 4a½-b½ Если можно то с полным решением

Answer 1

1. a1/2-b1/2=(a1/4-b1/4)(a1/4+b1/4)
2. a1/3-b1/3=(a1/6-b1/6)(a1/6+b1/6)
3. 4a1/2-b1/2=(2a1/4-b1/4)(2a1/4+b1/4)
Cтепень в скобках всегда в два раза меньше

Answer 2

Factoring using the identity a² - b² = (a + b)(a - b):

1) Factoring a½ - b½: To factor a½ - b½, we can rewrite it as (a½)² - (b½)². Now we have a difference of squares, which can be factored using the identity mentioned above. Applying the identity, we get:

a½ - b½ = (a½ + b½)(a½ - b½) [[1]]

2) Factoring a⅓ - b⅓: To factor a⅓ - b⅓, we can rewrite it as (a⅓)³ - (b⅓)³. Again, we have a difference of cubes, which can be factored using the identity mentioned above. Applying the identity, we get:

a⅓ - b⅓ = (a⅓ + b⅓)(a²/³ - a⅓b⅓ + b²/³) [[2]]

3) Factoring 4a½ - b½: To factor 4a½ - b½, we can rewrite it as (2a½)² - (b½)². Once again, we have a difference of squares, which can be factored using the identity mentioned above. Applying the identity, we get:

4a½ - b½ = (2a½ + b½)(2a½ - b½) [[3]]

Complete solutions:

1) Factoring a½ - b½: Using the factoring identity, we have:

a½ - b½ = (a½ + b½)(a½ - b½)

2) Factoring a⅓ - b⅓: Using the factoring identity, we have:

a⅓ - b⅓ = (a⅓ + b⅓