Question

(х - 10)(х² + 100)(х + 10)​

Answer 1

Ответ:

(x-10)(x²+100)(x+10) = (x²+100)(x²-100) = x⁴-10000

Использовалась формула: а²-b²=(a-b)(a+b)

Answer 2

$(x-10)(x^{2} +100)(x+10)=(x-10)(x+10)(x^{2} +100)=(x^{2} -10^{2}) (x^{2} +100)=(x^{2} -100)(x^{2} +100)=(x^{2} )^{2} -100^{2} =x^{2*2} -10000=x^{4} -10000.$

⇔ $(a-b)(a+b)=a^{2} -b^{2}$⇔

Answer 3

To multiply the given expression (x - 10)(x² + 100)(x + 10), you can use the distributive property to multiply each pair of factors. Here's how you can do it step by step:

1. Start by multiplying the first two factors, (x - 10) and (x² + 100):

   (x - 10)(x² + 100) = x(x²) + x(100) - 10(x²) - 10(100)

2. Now, multiply each term:

   x³ + 100x - 10x² - 1000

3. Next, multiply the result from step 2 by the third factor, (x + 10):

   (x³ + 100x - 10x² - 1000)(x + 10)

4. Apply the distributive property again:

   x(x³) + x(100x) + x(-10x²) + x(-1000) + 10(x³) + 10(100x) + 10(-10x²) + 10(-1000)

5. Multiply each term:

   x⁴ + 100x² - 10x³ - 1000x + 10x³ + 1000x - 100x² - 10000

6. Now, simplify the expression by combining like terms:

   x⁴ + 100x² - 10x³ - 1000x + 10x³ + 1000x - 100x² - 10000

   The terms -10x³ and 10x³ cancel each other out, as do -1000x and 1000x:

   x⁴ - 10000

So, the simplified expression is:

x⁴ - 10000