is this correct...
(3x^2+4x-3)^2-(3x^2-x+2)^2
then is it this
(9x^4+24x^3-2x^2-24x+9)-(9x^4-6x^3+13x^2-4x+4)
or this
9x^4+24x^3-2x^2-24x+9-9x^4-6x^3+13x^2-4x+4
should it have brakets or not that's my only problem
thanks
To correctly simplify the expression (3x^2+4x-3)^2-(3x^2-x+2)^2, you can apply the concept of expanding and combining like terms. Let's break it down step by step:
1. Expand both binomials using the formula for the square of a binomial:
(3x^2 + 4x - 3)^2 = (3x^2 + 4x - 3)(3x^2 + 4x - 3)
= 9x^4 + 12x^3 - 9x^2 + 12x^3 + 16x^2 - 12x - 9x^2 - 12x + 9
= 9x^4 + 24x^3 - 2x^2 - 24x + 9
(3x^2 - x + 2)^2 = (3x^2 - x + 2)(3x^2 - x + 2)
= 9x^4 - 3x^3 + 6x^2 - 3x^3 + x^2 - 2x + 6x^2 - 2x + 4
= 9x^4 - 6x^3 + 13x^2 - 4x + 4
2. Subtract the second expression from the first:
(9x^4 + 24x^3 - 2x^2 - 24x + 9) - (9x^4 - 6x^3 + 13x^2 - 4x + 4)
Now, there is no need for brackets in this case, since subtraction is already indicated by the operation symbols. Thus, you can simplify it further:
9x^4 + 24x^3 - 2x^2 - 24x + 9 - 9x^4 + 6x^3 - 13x^2 + 4x - 4
3. Combine like terms:
The x^4 terms (9x^4 - 9x^4) cancel out, as well as the x^3 terms (24x^3 - 6x^3). The remaining terms can be added together:
(24x^3 - 6x^3) = 18x^3
(-2x^2 - 13x^2) = -15x^2
(-24x + 4x) = -20x
(9 - 4) = 5
Therefore, the final simplified expression is:
18x^3 - 15x^2 - 20x + 5