Simplify the polynomial [(6x-8)-2x]-[(12x-7)-(4x-5)].
I came up with two answers:
36x^2 - 72x + 35 or
-12x^2 + 8x - 2
Are either one of these the correct answer?
To simplify the given polynomial [(6x-8)-2x]-[(12x-7)-(4x-5)], we need to simplify each individual expression within the brackets before performing the subtraction.
First, let's simplify the expression in the first set of brackets [(6x-8)-2x]:
6x - 8 - 2x = 4x - 8.
Next, let's simplify the expression in the second set of brackets [(12x-7)-(4x-5)]:
12x - 7 - 4x + 5 = 8x - 2.
Now, we can rearrange the remaining expression: (4x - 8) - (8x - 2).
Distribute the negative sign to the terms in the second set of brackets:
4x - 8 - 8x + 2.
Combine like terms:
(4x - 8x) + (-8 + 2) = -4x - 6.
Therefore, the simplified form of the expression [(6x-8)-2x]-[(12x-7)-(4x-5)] is -4x - 6. So, neither of the options presented (36x^2 - 72x + 35 or -12x^2 + 8x - 2) is correct.
To simplify the given polynomial [(6x-8)-2x]-[(12x-7)-(4x-5)], we need to follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
Let's proceed step by step:
Step 1: Simplify within the innermost set of parentheses:
(6x-8)-2x = 6x - 8 - 2x = 4x - 8
(12x-7)-(4x-5) = 12x - 7 - 4x + 5 = 8x - 2
Now, we have [(4x - 8) - (8x - 2)]. To simplify further, we distribute the negative sign to the terms inside the second set of parentheses:
[(4x - 8) - (8x - 2)] = 4x - 8 - 8x + 2
Step 2: Combine like terms:
(4x - 8 - 8x + 2) = (4x - 8x) + (-8 + 2) = -4x - 6
Therefore, the simplified form of the given polynomial is -4x - 6.
Neither of the answers you provided, 36x^2 - 72x + 35 or -12x^2 + 8x - 2, is correct.
let's see...
[(6x-8)-2x]-[(12x-7)-(4x-5)]
[6x-8-2x]-[12x-7-4x+5]
[4x-8]-[8x-2]
4x-8-8x+2
-8x-6
Unless you have dropped some exponents or mistyped some operators ...