Question

(x+2y)^3 Примени формулу куб суммы

Answer 1

Объяснение:

Раскроем скобки, применяя формулу сокращенного умножения.

$(a+b)^{3} =a^{3} +3a^{2} b+3ab^{2} +b^{3} .$

Тогда получим

$(x+2y)^{3} =x^{3} +3*x^{2} *2y+3*x*(2y)^{2} +(2y)^{3} =\\\\x^{3} +6x^{2} y+3x*4y^{2} +8y^{3} =x^{3} +6x^{2} y+12xy^{2} +8y^{3} .$

Answer 2

To expand the cube of the sum $(x + 2y)^3$, we can use the formula for the cube of a sum:

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

In this case, $a = x$ and $b = 2y$, so let's apply the formula:

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

Now, let's simplify the terms:

1. $x^3$.
2. $3x^2(2y) = 6x^2y$.
3. $3x(2y)^2 = 3x(4y^2) = 12xy^2$.
4. $(2y)^3 = 8y^3$.

Now, put all the simplified terms together:

$(x + 2y)^3 = x^3 + 6x^2y + 12xy^2 + 8y^3$.

So, the cube of the sum $(x + 2y)^3$ is $x^3 + 6x^2y + 12xy^2 + 8y^3$.