Question

Решите (y+3)^3 ; (a-c)^3 ; (c+d)^3

Answer 1

1)(y+3)^3=y^3+3y^2×3+3y+3^2+3^3=y^3+9y^2+3y×9+27=y^3+9y^2+27y+27

2)(a-c)^3=a^3-3a^2c+3ac^2-c^3

3)(y+3)^3=y^3+3y^2×3+3y×3^2+3^3=y^3+9y^2+3y×9+27=y^3+9y^2+27y+27

Answer 2

To simplify each of the expressions, we need to expand them using the binomial cube formula. The formula for expanding (x + y)^3 is:

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

Now, let's apply this formula to each expression:

1. (y + 3)^3: (y + 3)^3 = y^3 + 3y^2 * 3 + 3y * 3^2 + 3^3 = y^3 + 9y^2 + 27y + 27

2. (a - c)^3: (a - c)^3 = a^3 + 3a^2 * (-c) + 3a * (-c)^2 + (-c)^3 = a^3 - 3a^2c + 3ac^2 - c^3

3. (c + d)^3: (c + d)^3 = c^3 + 3c^2 * d + 3c * d^2 + d^3 = c^3 + 3c^2d + 3cd^2 + d^3

So, the simplified expressions are:

1. (y + 3)^3 = y^3 + 9y^2 + 27y + 27
2. (a - c)^3 = a^3 - 3a^2c + 3ac^2 - c^3
3. (c + d)^3 = c^3 + 3c^2d + 3cd^2 + d^3