Question

(x+1)(x+3)(x+5)(x+7)+10

Answer 1

Ответ:

26x

Пошаговое объяснение:

Answer 2

To expand the expression $(x+1)(x+3)(x+5)(x+7)+10$, you can use the distributive property to multiply each pair of factors and then combine like terms. Here's the step-by-step expansion:

1. First, expand $(x+1)(x+3)$: $(x+1)(x+3) = x(x+3) + 1(x+3) = x^2 + 3x + x + 3 = x^2 + 4x + 3$

2. Next, expand $(x^2 + 4x + 3)(x+5)$: $(x^2 + 4x + 3)(x+5) = x^2(x+5) + 4x(x+5) + 3(x+5)$ $= x^3 + 5x^2 + 4x^2 + 20x + 3x + 15$ $= x^3 + 9x^2 + 23x + 15$

3. Finally, expand $(x^3 + 9x^2 + 23x + 15)(x+7)$: $(x^3 + 9x^2 + 23x + 15)(x+7) = x^3(x+7) + 9x^2(x+7) + 23x(x+7) + 15(x+7)$ $= x^4 + 7x^3 + 9x^2(x+7) + 23x(x+7) + 15(x+7)$ $= x^4 + 7x^3 + 9x^3 + 63x^2 + 23x^2 + 161x + 15x + 105$ $= x^4 + 16x^3 + 86x^2 + 176x + 105$

Now, add the constant term 10 to this result:

$(x^4 + 16x^3 + 86x^2 + 176x + 105) + 10 = x^4 + 16x^3 + 86x^2 + 176x + 115$

So, the expanded expression is $x^4 + 16x^3 + 86x^2 + 176x + 115$.