Question

(2x-3y)(4x^2+6xy+9y^2)(8x^3+27y^3)

Answer 1

Ответ:

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Answer 2

To simplify the given expression $(2x-3y)(4x^2+6xy+9y^2)(8x^3+27y^3)$, you can perform a series of multiplications using the distributive property. Let's break it down step by step:

1. Multiply the first two factors: $(2x-3y)(4x^2+6xy+9y^2)$

   Use the distributive property (FOIL method) to multiply the terms:

   $$\begin{align*} &(2x-3y)(4x^2+6xy+9y^2) \\ &= 2x \cdot (4x^2+6xy+9y^2) - 3y \cdot (4x^2+6xy+9y^2) \\ &= 8x^3 + 12x^2y + 18xy^2 - 12x^2y - 18xy^2 - 27y^3 \\ &= 8x^3 - 27y^3 \end{align*}$$

2. Now, multiply the result by the third factor: $8x^3+27y^3$

   Multiply each term in the result by $8x^3+27y^3$:

   $$\begin{align*} &(8x^3 - 27y^3)(8x^3+27y^3) \\ &= 8x^3 \cdot 8x^3 + 8x^3 \cdot 27y^3 - 27y^3 \cdot 8x^3 - 27y^3 \cdot 27y^3 \\ &= 64x^6 + 216x^3y^3 - 216x^3y^3 - 729y^6 \\ &= 64x^6 - 729y^6 \end{align*}$$

So, the simplified expression is $64x^6 - 729y^6$.