Question

Помогите пожалуйста. Раскройте скобки a) (x-2)^2 b) (3x^2+y^2)^3

Answer 1

А) (x-2)^2 = x^2 - 4x +4
Б) (3x^2+y^2)^3 = 27x^6+ 9x^4*y^2+ 9x^2*y^4 + y^6

Answer 2

a) (x-2)^2

To expand the expression (x-2)^2, we can use the formula for squaring a binomial:

(a - b)^2 = a^2 - 2ab + b^2

In this case, a = x and b = 2. So, substituting these values into the formula, we get:

(x-2)^2 = x^2 - 2(x)(2) + 2^2

Simplifying further:

(x-2)^2 = x^2 - 4x + 4

Therefore, the expanded form of (x-2)^2 is x^2 - 4x + 4.

b) (3x^2+y^2)^3

To expand the expression (3x^2+y^2)^3, we can use the formula for cubing a binomial:

(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

In this case, a = 3x^2 and b = y^2. So, substituting these values into the formula, we get:

(3x^2+y^2)^3 = (3x^2)^3 + 3(3x^2)^2(y^2) + 3(3x^2)(y^2)^2 + (y^2)^3

Simplifying further:

(3x^2+y^2)^3 = 27x^6 + 27x^4y^2 + 9x^2y^4 + y^6

Therefore, the expanded form of (3x^2+y^2)^3 is 27x^6 + 27x^4y^2 + 9x^2y^4 + y^6.

I hope this helps! If you have any more questions, feel free to ask.