Question

(x+1)^2 (x-1)^2(x-2)^2(x+4)^2​

Answer 1

(х+1)²=х²+2х+1
(х-1)²=х²-2х+1
(х-2)²=х²-4х+4
(х+4)²=х²+8х+16Ответ:

Пошаговое объяснение:

Answer 2

To expand the expression $(x+1)^2(x-1)^2(x-2)^2(x+4)^2$, we can use the binomial expansion theorem and simplify it step by step.

First, let's expand $(x+1)^2$:

$(x+1)^2 = (x+1)(x+1) = x(x+1) + 1(x+1) = x^2 + x + x + 1 = x^2 + 2x + 1$

Next, we'll expand $(x-1)^2$:

$(x-1)^2 = (x-1)(x-1) = x(x-1) - 1(x-1) = x^2 - x - x + 1 = x^2 - 2x + 1$

Now, let's expand $(x-2)^2$:

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

Lastly, we'll expand $(x+4)^2$:

$(x+4)^2 = (x+4)(x+4) = x(x+4) + 4(x+4) = x^2 + 4x + 4x + 16 = x^2 + 8x + 16$

Now, we can multiply all the expanded expressions together:

$(x+1)^2(x-1)^2(x-2)^2(x+4)^2 = (x^2 + 2x + 1)(x^2 - 2x + 1)(x^2 - 4x + 4)(x^2 + 8x + 16)$

To simplify this further, we can multiply the terms together, combining like terms:

$(x^2 + 2x + 1)(x^2 - 2x + 1)(x^2 - 4x + 4)(x^2 + 8x + 16)$

Expanding and simplifying this expression would result in a very long polynomial. If you need the complete expansion, please let me know, and I'll be happy to provide it.