Question

(x+3)^3-(x-4)^3=21x^2+7

Answer 1

X^3 + 9x^2 + 27x + 27 - (x^3 -12x^2 +48x - 64) = 21x^2 + 7
x^3 + 9x^2 + 27x + 27 - x^3 + 12x^2 - 48x + 64 = 21x^2 + 7
21x^2 - 21x + 91 = 21x^2 + 7
-21x = 7 - 91
-21x = - 84
x = -84 : (-21)
x = 4

Answer 2

21*x^2-21*x+91 = 21*x^2+7

-21x = -84

x=4

Answer 3

Let's simplify the given expression step by step to verify if the equation holds true:

1. Expand the cubes using the formula (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3:

(x+3)^3 = x^3 + 3x^2*3 + 3x*3^2 + 3^3 = x^3 + 9x^2 + 27x + 27

(x-4)^3 = x^3 - 3x^2*4 + 3x*4^2 - 4^3 = x^3 - 12x^2 + 48x - 64

2. Substitute the expanded expressions back into the original equation:

(x+3)^3 - (x-4)^3 = (x^3 + 9x^2 + 27x + 27) - (x^3 - 12x^2 + 48x - 64)

3. Simplify by combining like terms:

(x^3 + 9x^2 + 27x + 27) - (x^3 - 12x^2 + 48x - 64) = x^3 + 9x^2 + 27x + 27 - x^3 + 12x^2 - 48x + 64

4. The x^3 term cancels out:

x^3 - x^3 = 0

5. Combine like terms:

9x^2 + 12x^2 + 27x - 48x + 27 + 64 = 21x^2 + 7

6. Simplify further:

21x^2 - 21x + 91 = 21x^2 + 7

At this point, we see that the equation does not hold true. When simplifying the given expression, we end up with 21x^2 - 21x + 91 = 21x^2 + 7, and as you can see, the x terms on both sides do not cancel out. Therefore, the original equation (x+3)^3 - (x-4)^3 = 21x^2 + 7 is not true.