Question

100^3 - 90^3. Решите с помощью формулы сокращённого умножения.

Answer 1

100³-90³=(100-90)*(100²+100*90+90²)=10*(10000+9000+8100)=10*27100= 271000

Answer 2

To simplify the expression $100^3 - 90^3$ using the formula for the difference of cubes, we can use the following identity:

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

In this case, $a = 100$ and $b = 90$. Let's plug in these values:

$100^3 - 90^3 = (100 - 90)(100^2 + 100 \times 90 + 90^2)$

Now, let's calculate the values:

1. $100 - 90 = 10$
2. $100^2 = 100 \times 100 = 10000$
3. $100 \times 90 = 9000$
4. $90^2 = 90 \times 90 = 8100$

Now, substitute these values back into the equation:

$100^3 - 90^3 = 10 \times (10000 + 9000 + 8100)$

Next, calculate the sum inside the parentheses:

$10000 + 9000 + 8100 = 27100$

Finally, calculate the result:

$100^3 - 90^3 = 10 \times 27100 = 271000$

So, $100^3 - 90^3 = 271000$.