Question

(x+5)^3-(x+1)^3-4(3x^2-5)+10x-7

Answer 1

(х+5)³-(х+1)³-4(3х²-5)+10х-7=0+82х+137=82х+137

Answer 2

Разложили, раскрыли скобки, вычислили

Answer 3

To simplify the given expression, let's start by expanding the cubes and then combine like terms:

Step 1: Expand the cubes. Recall the formula for expanding (a + b)^3: (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

Now, let's apply this formula to each cube in the expression:

1. (x + 5)^3 = x^3 + 3x^2 * 5 + 3x * 5^2 + 5^3 = x^3 + 15x^2 + 75x + 125

2. (x + 1)^3 = x^3 + 3x^2 * 1 + 3x * 1^2 + 1^3 = x^3 + 3x^2 + 3x + 1

Step 2: Combine like terms. Now, let's substitute the expanded cubes back into the original expression and simplify:

(x + 5)^3 - (x + 1)^3 - 4(3x^2 - 5) + 10x - 7

= (x^3 + 15x^2 + 75x + 125) - (x^3 + 3x^2 + 3x + 1) - 4(3x^2 - 5) + 10x - 7

= x^3 + 15x^2 + 75x + 125 - x^3 - 3x^2 - 3x - 1 - 12x^2 + 20 + 10x - 7

Now, let's combine like terms:

= (x^3 - x^3) + (15x^2 - 3x^2 - 12x^2) + (75x + 10x - 3x) + (125 - 1 + 20 - 7)

= 0 + 0x^2 + 82x + 137

So, the simplified expression is: 82x + 137